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The cohomology of commutative semigroups : an overview / / Pierre Antoine Grillet
The cohomology of commutative semigroups : an overview / / Pierre Antoine Grillet
Autore Grillet Pierre A (Pierre Antoine), <1941->
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (191 pages)
Disciplina 514.23
Collana Lecture Notes in Mathematics
Soggetto topico Cohomology operations
Commutative semigroups
Homologia
Soggetto genere / forma Llibres electrònics
ISBN 9783031082122
9783031082115
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- List of Symbols -- 1 The Beginning -- 1.1 The Congruence H -- 1.1.1 Basics -- 1.1.2 Commutative Group Coextensions -- 1.2 Construction -- 1.2.1 Schreier's Method -- 1.2.2 Split Coextensions -- 1.2.3 Enter Cohomology -- 1.2.4 Finite Semigroups -- 2 Beck Cohomology -- 2.1 General Beck Cohomology -- 2.1.1 Simple Cohomology -- 2.1.2 Abelian Group Objects -- 2.1.3 Objects Over S -- 2.1.4 Beck Cohomology -- 2.1.5 Main Properties -- 2.1.6 Beck Extensions -- 2.2 Commutative Semigroups -- 2.2.1 Commutative Semigroups Over S -- 2.2.2 Abelian Group Objects Over S -- 2.2.3 Beck Extensions of S -- 2.3 Beck Cohomology of Commutative Semigroups -- 2.3.1 The `Free Commutative Semigroup' Adjunction -- 2.3.2 The `Free Commutative Semigroup' Comonad -- 2.3.3 Cochains -- 2.3.4 Cohomology -- 2.3.5 Properties -- 3 Symmetric Cohomology -- 3.1 Definition -- 3.1.1 Cochains -- 3.1.2 Symmetric Cochains -- 3.1.3 Symmetric Cohomology -- 3.1.4 An Example -- 3.2 Comparison with Beck Cohomology -- 3.2.1 Dimension 1 -- 3.2.2 Dimension 2 -- 3.2.3 Dimensions 3 and 4 -- 3.3 Main Properties -- 3.4 Normalization -- 3.4.1 Dimension 2 -- 3.4.2 Dimension 3 -- 4 Calvo-Cegarra Cohomology -- 4.1 Small Categories -- 4.2 Cohomology of Simplicial Sets -- 4.2.1 Definition -- 4.2.2 Cochains -- 4.2.3 The Classifying Simplicial Set -- 4.3 Cohomology of Commutative Semigroups -- 4.3.1 The Double Classifying Simplicial Set -- 4.3.2 Cochains -- 4.4 Extended Cochains -- 4.4.1 Definition -- 4.4.2 Comparison with Symmetric Cohomology -- 4.4.3 An Example -- 4.5 Properties -- 5 The Third Cohomology Group -- 5.1 Groupoids -- 5.1.1 Groupoids -- 5.1.2 Monoidal Groupoids -- 5.1.3 Reduction -- 5.1.4 The Base -- 5.2 Symmetric 3-Cocycles -- 5.2.1 Cocycle Objects -- 5.2.2 Morphisms -- 5.3 Classification -- 5.3.1 Isomorphisms -- 5.3.2 Equivalence -- 5.3.3 Lone Cocycles.
5.4 Braided Groupoids -- 5.4.1 Definition -- 5.4.2 Reduction -- 5.4.3 The Base -- 5.4.4 Extended Cocycle Objects -- 5.4.5 Classification -- 6 The Overpath Method -- 6.1 Paths and Overpaths -- 6.1.1 Free Commutative Monoids -- 6.1.2 Congruences -- 6.1.3 Paths -- 6.1.4 Overpaths -- 6.2 Main Result -- 6.2.1 Minimal Cocycles -- 6.2.2 Main Result -- 6.2.3 Examples -- 6.2.4 Semigroups with One Relator -- 6.3 Other Results -- 6.3.1 Branching -- 6.3.2 Relations -- 6.3.3 Partially Free Semigroups -- 6.3.4 Nilmonoids -- 6.3.5 Semigroups with Zero Cohomology -- 7 Symmetric Chains -- 7.1 Symmetric Mappings -- 7.1.1 Symmetry -- 7.1.2 Bases -- 7.2 Chain Groups -- 7.2.1 Definition -- 7.2.2 Properties -- 7.2.3 Symmetric n-chains -- 7.3 Chain Functors -- 7.3.1 Thin Chain Functors -- 7.3.2 General Chain Functors -- 7.4 Semiconstant Functors -- 7.4.1 Definition -- 7.4.2 Chain Groups -- 7.4.3 Properties -- 7.4.4 Homology -- 7.4.5 Cohomology -- 8 Inheritance -- 8.1 The Universal Coboundary -- 8.1.1 Symmetry Properties -- 8.1.2 The Universal Coboundary -- 8.1.3 The Group D -- 8.2 One Equality Between Variables -- 8.3 Results -- 8.3.1 Method -- 8.3.2 Order 5 -- 8.3.3 Other Orders -- 9 Appendixes -- 9.1 Extensions -- 9.1.1 Group Extensions -- 9.1.2 Rédei Extensions -- 9.1.3 The Leech Categories -- 9.1.4 Cosets -- 9.1.5 Group Coextensions -- 9.1.6 Congruences Contained in H -- 9.1.7 Leech Coextensions -- 9.1.8 Leech Cohomology -- 9.2 Monads and Algebras -- 9.2.1 Adjunctions -- 9.2.2 Monads -- 9.2.3 Algebras -- 9.3 Simplicial Objects -- 9.3.1 Simplicial Sets -- 9.3.2 The Simplicial Category -- 9.3.3 The Classifying Simplicial Set -- 9.3.4 Cohomology -- 9.4 Monoidal Categories -- 9.4.1 Strict Monoidal Categories -- 9.4.2 General Monoidal Categories -- 9.4.3 Monoidal Functors -- 9.4.4 Braided Monoidal Categories -- 9.5 Modules -- 9.5.1 S-Modules -- 9.5.2 Quasiconstant Functors.
9.5.3 Conclusions -- References -- Index.
Record Nr. UNISA-996490345203316
Grillet Pierre A (Pierre Antoine), <1941->  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
The cohomology of commutative semigroups : an overview / / Pierre Antoine Grillet
The cohomology of commutative semigroups : an overview / / Pierre Antoine Grillet
Autore Grillet Pierre A (Pierre Antoine), <1941->
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (191 pages)
Disciplina 514.23
Collana Lecture Notes in Mathematics
Soggetto topico Cohomology operations
Commutative semigroups
Homologia
Soggetto genere / forma Llibres electrònics
ISBN 9783031082122
9783031082115
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- List of Symbols -- 1 The Beginning -- 1.1 The Congruence H -- 1.1.1 Basics -- 1.1.2 Commutative Group Coextensions -- 1.2 Construction -- 1.2.1 Schreier's Method -- 1.2.2 Split Coextensions -- 1.2.3 Enter Cohomology -- 1.2.4 Finite Semigroups -- 2 Beck Cohomology -- 2.1 General Beck Cohomology -- 2.1.1 Simple Cohomology -- 2.1.2 Abelian Group Objects -- 2.1.3 Objects Over S -- 2.1.4 Beck Cohomology -- 2.1.5 Main Properties -- 2.1.6 Beck Extensions -- 2.2 Commutative Semigroups -- 2.2.1 Commutative Semigroups Over S -- 2.2.2 Abelian Group Objects Over S -- 2.2.3 Beck Extensions of S -- 2.3 Beck Cohomology of Commutative Semigroups -- 2.3.1 The `Free Commutative Semigroup' Adjunction -- 2.3.2 The `Free Commutative Semigroup' Comonad -- 2.3.3 Cochains -- 2.3.4 Cohomology -- 2.3.5 Properties -- 3 Symmetric Cohomology -- 3.1 Definition -- 3.1.1 Cochains -- 3.1.2 Symmetric Cochains -- 3.1.3 Symmetric Cohomology -- 3.1.4 An Example -- 3.2 Comparison with Beck Cohomology -- 3.2.1 Dimension 1 -- 3.2.2 Dimension 2 -- 3.2.3 Dimensions 3 and 4 -- 3.3 Main Properties -- 3.4 Normalization -- 3.4.1 Dimension 2 -- 3.4.2 Dimension 3 -- 4 Calvo-Cegarra Cohomology -- 4.1 Small Categories -- 4.2 Cohomology of Simplicial Sets -- 4.2.1 Definition -- 4.2.2 Cochains -- 4.2.3 The Classifying Simplicial Set -- 4.3 Cohomology of Commutative Semigroups -- 4.3.1 The Double Classifying Simplicial Set -- 4.3.2 Cochains -- 4.4 Extended Cochains -- 4.4.1 Definition -- 4.4.2 Comparison with Symmetric Cohomology -- 4.4.3 An Example -- 4.5 Properties -- 5 The Third Cohomology Group -- 5.1 Groupoids -- 5.1.1 Groupoids -- 5.1.2 Monoidal Groupoids -- 5.1.3 Reduction -- 5.1.4 The Base -- 5.2 Symmetric 3-Cocycles -- 5.2.1 Cocycle Objects -- 5.2.2 Morphisms -- 5.3 Classification -- 5.3.1 Isomorphisms -- 5.3.2 Equivalence -- 5.3.3 Lone Cocycles.
5.4 Braided Groupoids -- 5.4.1 Definition -- 5.4.2 Reduction -- 5.4.3 The Base -- 5.4.4 Extended Cocycle Objects -- 5.4.5 Classification -- 6 The Overpath Method -- 6.1 Paths and Overpaths -- 6.1.1 Free Commutative Monoids -- 6.1.2 Congruences -- 6.1.3 Paths -- 6.1.4 Overpaths -- 6.2 Main Result -- 6.2.1 Minimal Cocycles -- 6.2.2 Main Result -- 6.2.3 Examples -- 6.2.4 Semigroups with One Relator -- 6.3 Other Results -- 6.3.1 Branching -- 6.3.2 Relations -- 6.3.3 Partially Free Semigroups -- 6.3.4 Nilmonoids -- 6.3.5 Semigroups with Zero Cohomology -- 7 Symmetric Chains -- 7.1 Symmetric Mappings -- 7.1.1 Symmetry -- 7.1.2 Bases -- 7.2 Chain Groups -- 7.2.1 Definition -- 7.2.2 Properties -- 7.2.3 Symmetric n-chains -- 7.3 Chain Functors -- 7.3.1 Thin Chain Functors -- 7.3.2 General Chain Functors -- 7.4 Semiconstant Functors -- 7.4.1 Definition -- 7.4.2 Chain Groups -- 7.4.3 Properties -- 7.4.4 Homology -- 7.4.5 Cohomology -- 8 Inheritance -- 8.1 The Universal Coboundary -- 8.1.1 Symmetry Properties -- 8.1.2 The Universal Coboundary -- 8.1.3 The Group D -- 8.2 One Equality Between Variables -- 8.3 Results -- 8.3.1 Method -- 8.3.2 Order 5 -- 8.3.3 Other Orders -- 9 Appendixes -- 9.1 Extensions -- 9.1.1 Group Extensions -- 9.1.2 Rédei Extensions -- 9.1.3 The Leech Categories -- 9.1.4 Cosets -- 9.1.5 Group Coextensions -- 9.1.6 Congruences Contained in H -- 9.1.7 Leech Coextensions -- 9.1.8 Leech Cohomology -- 9.2 Monads and Algebras -- 9.2.1 Adjunctions -- 9.2.2 Monads -- 9.2.3 Algebras -- 9.3 Simplicial Objects -- 9.3.1 Simplicial Sets -- 9.3.2 The Simplicial Category -- 9.3.3 The Classifying Simplicial Set -- 9.3.4 Cohomology -- 9.4 Monoidal Categories -- 9.4.1 Strict Monoidal Categories -- 9.4.2 General Monoidal Categories -- 9.4.3 Monoidal Functors -- 9.4.4 Braided Monoidal Categories -- 9.5 Modules -- 9.5.1 S-Modules -- 9.5.2 Quasiconstant Functors.
9.5.3 Conclusions -- References -- Index.
Record Nr. UNINA-9910616380303321
Grillet Pierre A (Pierre Antoine), <1941->  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Equivariant cohomology of configuration spaces Mod 2 : the state of the art / / Pavle V. M. Blagojević [and four others]
Equivariant cohomology of configuration spaces Mod 2 : the state of the art / / Pavle V. M. Blagojević [and four others]
Autore Blagojević Pavle V. M.
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (217 pages)
Disciplina 514.23
Collana Lecture Notes in Mathematics
Soggetto topico Homologia
Cohomology operations
Algebraic topology
Soggetto genere / forma Llibres electrònics
ISBN 3-030-84138-3
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466562003316
Blagojević Pavle V. M.  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Equivariant Poincaré duality on G-manifolds : equivariant Gysin morphism and equivariant Euler classes / / Alberto Arabia
Equivariant Poincaré duality on G-manifolds : equivariant Gysin morphism and equivariant Euler classes / / Alberto Arabia
Autore Arabia Alberto
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XV, 376 p. 272 illus., 2 illus. in color.)
Disciplina 515.782
Collana Lecture Notes in Mathematics
Soggetto topico Duality theory (Mathematics)
Cohomology operations
Teoria de la dualitat (Matemàtica)
Homologia
Soggetto genere / forma Llibres electrònics
ISBN 3-030-70440-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910483511503321
Arabia Alberto  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Equivariant Poincaré duality on G-manifolds : equivariant Gysin morphism and equivariant Euler classes / / Alberto Arabia
Equivariant Poincaré duality on G-manifolds : equivariant Gysin morphism and equivariant Euler classes / / Alberto Arabia
Autore Arabia Alberto
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XV, 376 p. 272 illus., 2 illus. in color.)
Disciplina 515.782
Collana Lecture Notes in Mathematics
Soggetto topico Duality theory (Mathematics)
Cohomology operations
Teoria de la dualitat (Matemàtica)
Homologia
Soggetto genere / forma Llibres electrònics
ISBN 3-030-70440-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466402203316
Arabia Alberto  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Helix Structures in Quantum Cohomology of Fano Varieties / / by Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti
Helix Structures in Quantum Cohomology of Fano Varieties / / by Giordano Cotti, Boris A. Dubrovin, Davide Guzzetti
Autore Cotti Giordano
Edizione [1st ed. 2024.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024
Descrizione fisica 1 online resource (241 pages)
Disciplina 516.35
Altri autori (Persone) DubrovinBoris A
GuzzettiDavide
Collana Lecture Notes in Mathematics
Soggetto topico Geometry, Algebraic
Mathematical physics
Differential equations
Geometry, Differential
Algebra, Homological
Algebraic Geometry
Mathematical Physics
Differential Equations
Differential Geometry
Category Theory, Homological Algebra
Categories (Matemàtica)
Geometria algebraica
Topologia algebraica
Homologia
Hèlices
Soggetto genere / forma Llibres electrònics
ISBN 3-031-69067-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto - Introduction -- Gromov–Witten Theory and Quantum Cohomology -- Helix Theory in Triangulated Categories -- Non-Symmetric Orthogonal Geometry of Mukai Lattices -- The Main Conjecture -- Proof of the Main Conjecture for Projective Spaces -- Proof of the Main Conjecture for Grassmannians.
Record Nr. UNINA-9910900176303321
Cotti Giordano  
Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Journal of homotopy and related structures
Journal of homotopy and related structures
Pubbl/distr/stampa Tbilisi : , : A. Razmadze Mathematical Institute, , ©2006-
Descrizione fisica 1 online resource
Soggetto topico Homology theory
Mathematical physics
Homologia
Física matemàtica
Soggetto genere / forma Periodicals.
Revistes electròniques
ISSN 2193-8407
Formato Materiale a stampa
Livello bibliografico Periodico
Lingua di pubblicazione eng
Altri titoli varianti JHRS
Record Nr. UNINA-9910307948103321
Tbilisi : , : A. Razmadze Mathematical Institute, , ©2006-
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Lagrangian Floer Theory and Its Deformations : An Introduction to Filtered Fukaya Category / / by Yong-Geun Oh
Lagrangian Floer Theory and Its Deformations : An Introduction to Filtered Fukaya Category / / by Yong-Geun Oh
Autore Oh Yong-Geun
Edizione [1st ed. 2024.]
Pubbl/distr/stampa Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2024
Descrizione fisica 1 online resource (426 pages)
Disciplina 516.36
Collana KIAS Springer Series in Mathematics
Soggetto topico Geometry, Differential
Algebraic topology
Topology
Differential Geometry
Algebraic Topology
Espais de llaços
Funcions de Lagrange
Homologia
Soggetto genere / forma Llibres electrònics
ISBN 9789819717989
9789819717972
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Based Loop Space and A∞ Space -- A∞ Algebras and Modules: Unfiltered Case -- Obstruction-Deformation Theory of Filtered A∞ Bimodules -- Symplectic Geometry and Hamiltonian Dynamics -- Analysis of Pseudoholomorphic Curves and Bordered Stable Maps -- Critical Points of Potential Functions and Floer Cohomology -- Filtered Fukaya Category and its Bulk Deformations.
Record Nr. UNINA-9910865256703321
Oh Yong-Geun  
Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Morse Homology with Differential Graded Coefficients / / by Jean-François Barraud, Mihai Damian, Vincent Humilière, Alexandru Oancea
Morse Homology with Differential Graded Coefficients / / by Jean-François Barraud, Mihai Damian, Vincent Humilière, Alexandru Oancea
Autore Barraud Jean-François
Edizione [1st ed. 2025.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025
Descrizione fisica 1 online resource (231 pages)
Disciplina 514.34
Altri autori (Persone) DamianMihai
HumilièreVincent
OanceaAlexandru
Collana Progress in Mathematics
Soggetto topico Manifolds (Mathematics)
Algebraic topology
Manifolds and Cell Complexes
Algebraic Topology
Topologia algebraica
Homologia
Teoria de Morse
Soggetto genere / forma Llibres electrònics
ISBN 3-031-88020-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Introduction and Main Results -- Morse vs DG Morse Homology Toolset -- Comparison of the Barraud-Cornea Cocycle and the Brown Cocycle -- Algebraic Properties of Twisted Complexes -- Morse Homology with DG-Coefficients: Construction -- Morse Homology with DG-Coefficients: Invariance -- Fibrations -- Functoriality: General Properties -- Functoriality: First Definition -- Functoriality: Second Definition. Cohomology and Poincaré Duality -- Shriek Maps and Poincaré Duality for Non-Orientable Manifolds -- Beyond the Case of Manifolds of Finite Dimension -- Appendix: Comparison of Geometry and Analytic Orientations in Morse Theory.
Record Nr. UNINA-9911007359003321
Barraud Jean-François  
Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2025
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Twisted Morse Complexes : Morse Homology and Cohomology with Local Coefficients / / by Augustin Banyaga, David Hurtubise, Peter Spaeth
Twisted Morse Complexes : Morse Homology and Cohomology with Local Coefficients / / by Augustin Banyaga, David Hurtubise, Peter Spaeth
Autore Banyaga Augustin
Edizione [1st ed. 2024.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024
Descrizione fisica 1 online resource (VIII, 158 p. 58 illus.)
Disciplina 515.39
Collana Lecture Notes in Mathematics
Soggetto topico Dynamics
Algebraic topology
Manifolds (Mathematics)
Global analysis (Mathematics)
Dynamical Systems
Algebraic Topology
Manifolds and Cell Complexes
Global Analysis and Analysis on Manifolds
Homologia
Teoria de Morse
Soggetto genere / forma Llibres electrònics
ISBN 3-031-71616-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto - 1. Introduction -- 2. The Morse Complex with Local Coefficients -- 3. The Homology Determined by the Isomorphism Class of G -- 4. Singular and CW-Homology with Local Coefficients -- 5. Twisted Morse Cohomology and Lichnerowicz Cohomology -- 6. Applications and Computations.
Record Nr. UNINA-9910903799103321
Banyaga Augustin  
Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2024
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui