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Algebraic Topology [[electronic resource] ] : VIASM 2012–2015 / / edited by H.V. Hưng Nguyễn, Lionel Schwartz
| Algebraic Topology [[electronic resource] ] : VIASM 2012–2015 / / edited by H.V. Hưng Nguyễn, Lionel Schwartz |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (VII, 180 p. 5 illus., 2 illus. in color.) |
| Disciplina | 514.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Algebraic topology
Category theory (Mathematics) Homological algebra Algebraic Topology Category Theory, Homological Algebra |
| ISBN | 3-319-69434-0 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Introduction -- Contents -- 1 Hodge Filtration and Operations in Higher Hochschild (Co)homology and Applications to Higher String Topology -- 1.1 Introduction and Overview -- 1.2 Notations, Conventions and a Few Standard Facts -- 1.3 Higher Hochschild (Co)homology -- 1.3.1 -Modules and Hochschild (Co)chain Complexes over Spaces -- 1.3.2 Combinatorial Higher Hochschild (Co)chains -- 1.3.3 Derived Hochschild (Co)chains -- 1.4 Hodge Filtration and λ-Operations on Hochschild (Co)homology over Spheres and Suspensions -- 1.4.1 γ-Rings and Lambda Operations -- 1.4.2 Edgewise Subdivision and Simplicial Approach to λ-Operations -- 1.4.3 Hodge Filtration for Hochschild Cochains over Spheres and Suspensions -- 1.4.4 Hodge Filtration on Hochschild Cochains on the Standard Model -- 1.4.5 Hodge Filtration and λ-Operations for Hochschild Chains over Spheres and Suspensions -- 1.4.6 Hodge Filtration and the Eilenberg-Zilber Model for Hochschild Cochains of Suspensions and Products -- 1.5 Additional Ring Structures for Higher Hochschild Cohomology -- 1.5.1 The Wedge and Cup Product -- 1.5.2 The Universal En-Algebra Structure Lifting the Cup-Product -- 1.5.2.1 The En-Structure of Hochschild (Co)homology over Sn -- 1.5.2.2 The Combinatorial Description of the Centralizer of CDGA Maps -- 1.5.3 The O(d)-Equivariance of the Universal Ed Algebra Structure on Hochschild Cochomology over Spheres -- 1.6 Applications of Higher Hochschild-Kostant-Rosenberg Theorem -- 1.6.1 Statement of HKR Theorem -- 1.6.2 HKR Isomorphism and Hodge Decomposition -- 1.6.3 Compatibility of Hodge Decomposition with the Algebra Structure in Cohomology and Induced Poisn+1-Algebra Structure -- 1.6.4 Applications to Poisn-Algebras (Co)homology -- 1.7 Applications to Brane Topology -- 1.7.1 Higher Hochschild (Co)homology as a Model for Mapping Spaces.
1.7.2 Models for Brane Topology in Characteristic Zero -- References -- 2 On the Derived Functors of Destabilization and of Iterated Loop Functors -- 2.1 Introduction -- 2.2 Background -- 2.2.1 The Steenrod Algebra as a Quadratic Algebra -- 2.2.2 The Category of A-Modules -- 2.2.3 Unstable Modules and Destabilization -- 2.2.4 Derived Functors -- 2.2.5 Motivation for Studying Derived Functors of Destabilization and of Iterated Loop Functors -- 2.3 First Results on Derived Functors of Destabilization and of Iterated Loops -- 2.3.1 Derived Functors of Ω -- 2.3.2 Applications of Ω and Ω1 -- 2.3.3 Interactions Between Loops and Destabilization -- 2.3.4 Connectivity for Ds -- 2.3.5 Comparing Ds and Ωts -- 2.4 Singer Functors -- 2.4.1 The Unstable Singer Functors Rs -- 2.4.2 Singer Functors for M -- 2.4.3 The Singer Differential -- 2.5 Constructing Chain Complexes -- 2.5.1 Destabilization -- 2.5.2 Iterated Loops -- 2.5.3 The Lannes-Zarati Homomorphism -- 2.6 Perspectives -- 2.6.1 The Spherical Class Conjecture and Related Problems -- 2.6.2 Generalizations of the Lannes-Zarati Homomorphism -- References -- 3 A Mini-Course on Morava Stabilizer Groups and Their Cohomology -- 3.1 Introduction -- 3.2 Bousfield Localization and the Chromatic Set Up -- 3.2.1 Bousfield Localization -- 3.2.2 Morava K-Theories -- 3.2.3 LK(n)S0 as Homotopy Fixed Point Spectrum -- 3.3 Resolutions of K(n)-Local Spheres -- 3.3.1 The Example n=1 and p>2 -- 3.3.2 The Case That p-1 Does Not Divide n -- 3.3.3 The Example n=2 and p>3 -- 3.3.4 The Example n=1 and p=2 -- 3.3.5 The General Case p-1 Divides n -- 3.3.6 The Example n=2 and p=3 -- 3.3.7 Permutation Resolutions and Realizations -- 3.3.8 Applications and Work in Progress -- 3.3.8.1 The Case n=2 and p=3 -- 3.3.8.2 The Case n=2 and p>3 -- 3.3.8.3 The Case n=p=2 -- 3.4 The Morava Stabilizer Groups: First Properties. 3.4.1 The Morava Stabilizer Group as a Profinite Group -- 3.4.2 The Associated Mixed Lie Algebra of Sn -- 3.4.3 Torsion in the Morava Stabilizer Groups -- 3.5 On the Cohomology of the Stabilizer Groups with Trivial Coefficients -- 3.5.1 H1: The Stabilizer Group Made Abelian -- 3.5.2 The Cohomology of S1 -- 3.5.3 Structural Properties of H*(Sn,Z/p) -- 3.5.4 The Reduced Norm and a Decomposition of Sn -- 3.5.5 Cohomology in Case n=2 and p>2 -- 3.5.5.1 The Case p>3 -- 3.5.5.2 The Case p=3 -- 3.5.5.3 The Case p=2 -- 3.6 Cohomology with Non-trivial Coefficients and Resolutions -- 3.6.1 The Case n=1 -- 3.6.1.1 The Case p>2 -- 3.6.1.2 The Case p=2 -- 3.6.2 Some Comments on the Case n=2 -- References. |
| Record Nr. | UNISA-996466537803316 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
| ||
Algebraic Topology : VIASM 2012–2015 / / edited by H.V. Hưng Nguyễn, Lionel Schwartz
| Algebraic Topology : VIASM 2012–2015 / / edited by H.V. Hưng Nguyễn, Lionel Schwartz |
| Edizione | [1st ed. 2017.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 |
| Descrizione fisica | 1 online resource (VII, 180 p. 5 illus., 2 illus. in color.) |
| Disciplina | 514.2 |
| Collana | Lecture Notes in Mathematics |
| Soggetto topico |
Algebraic topology
Categories (Mathematics) Algebra, Homological Algebraic Topology Category Theory, Homological Algebra |
| ISBN | 3-319-69434-0 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Intro -- Introduction -- Contents -- 1 Hodge Filtration and Operations in Higher Hochschild (Co)homology and Applications to Higher String Topology -- 1.1 Introduction and Overview -- 1.2 Notations, Conventions and a Few Standard Facts -- 1.3 Higher Hochschild (Co)homology -- 1.3.1 -Modules and Hochschild (Co)chain Complexes over Spaces -- 1.3.2 Combinatorial Higher Hochschild (Co)chains -- 1.3.3 Derived Hochschild (Co)chains -- 1.4 Hodge Filtration and λ-Operations on Hochschild (Co)homology over Spheres and Suspensions -- 1.4.1 γ-Rings and Lambda Operations -- 1.4.2 Edgewise Subdivision and Simplicial Approach to λ-Operations -- 1.4.3 Hodge Filtration for Hochschild Cochains over Spheres and Suspensions -- 1.4.4 Hodge Filtration on Hochschild Cochains on the Standard Model -- 1.4.5 Hodge Filtration and λ-Operations for Hochschild Chains over Spheres and Suspensions -- 1.4.6 Hodge Filtration and the Eilenberg-Zilber Model for Hochschild Cochains of Suspensions and Products -- 1.5 Additional Ring Structures for Higher Hochschild Cohomology -- 1.5.1 The Wedge and Cup Product -- 1.5.2 The Universal En-Algebra Structure Lifting the Cup-Product -- 1.5.2.1 The En-Structure of Hochschild (Co)homology over Sn -- 1.5.2.2 The Combinatorial Description of the Centralizer of CDGA Maps -- 1.5.3 The O(d)-Equivariance of the Universal Ed Algebra Structure on Hochschild Cochomology over Spheres -- 1.6 Applications of Higher Hochschild-Kostant-Rosenberg Theorem -- 1.6.1 Statement of HKR Theorem -- 1.6.2 HKR Isomorphism and Hodge Decomposition -- 1.6.3 Compatibility of Hodge Decomposition with the Algebra Structure in Cohomology and Induced Poisn+1-Algebra Structure -- 1.6.4 Applications to Poisn-Algebras (Co)homology -- 1.7 Applications to Brane Topology -- 1.7.1 Higher Hochschild (Co)homology as a Model for Mapping Spaces.
1.7.2 Models for Brane Topology in Characteristic Zero -- References -- 2 On the Derived Functors of Destabilization and of Iterated Loop Functors -- 2.1 Introduction -- 2.2 Background -- 2.2.1 The Steenrod Algebra as a Quadratic Algebra -- 2.2.2 The Category of A-Modules -- 2.2.3 Unstable Modules and Destabilization -- 2.2.4 Derived Functors -- 2.2.5 Motivation for Studying Derived Functors of Destabilization and of Iterated Loop Functors -- 2.3 First Results on Derived Functors of Destabilization and of Iterated Loops -- 2.3.1 Derived Functors of Ω -- 2.3.2 Applications of Ω and Ω1 -- 2.3.3 Interactions Between Loops and Destabilization -- 2.3.4 Connectivity for Ds -- 2.3.5 Comparing Ds and Ωts -- 2.4 Singer Functors -- 2.4.1 The Unstable Singer Functors Rs -- 2.4.2 Singer Functors for M -- 2.4.3 The Singer Differential -- 2.5 Constructing Chain Complexes -- 2.5.1 Destabilization -- 2.5.2 Iterated Loops -- 2.5.3 The Lannes-Zarati Homomorphism -- 2.6 Perspectives -- 2.6.1 The Spherical Class Conjecture and Related Problems -- 2.6.2 Generalizations of the Lannes-Zarati Homomorphism -- References -- 3 A Mini-Course on Morava Stabilizer Groups and Their Cohomology -- 3.1 Introduction -- 3.2 Bousfield Localization and the Chromatic Set Up -- 3.2.1 Bousfield Localization -- 3.2.2 Morava K-Theories -- 3.2.3 LK(n)S0 as Homotopy Fixed Point Spectrum -- 3.3 Resolutions of K(n)-Local Spheres -- 3.3.1 The Example n=1 and p>2 -- 3.3.2 The Case That p-1 Does Not Divide n -- 3.3.3 The Example n=2 and p>3 -- 3.3.4 The Example n=1 and p=2 -- 3.3.5 The General Case p-1 Divides n -- 3.3.6 The Example n=2 and p=3 -- 3.3.7 Permutation Resolutions and Realizations -- 3.3.8 Applications and Work in Progress -- 3.3.8.1 The Case n=2 and p=3 -- 3.3.8.2 The Case n=2 and p>3 -- 3.3.8.3 The Case n=p=2 -- 3.4 The Morava Stabilizer Groups: First Properties. 3.4.1 The Morava Stabilizer Group as a Profinite Group -- 3.4.2 The Associated Mixed Lie Algebra of Sn -- 3.4.3 Torsion in the Morava Stabilizer Groups -- 3.5 On the Cohomology of the Stabilizer Groups with Trivial Coefficients -- 3.5.1 H1: The Stabilizer Group Made Abelian -- 3.5.2 The Cohomology of S1 -- 3.5.3 Structural Properties of H*(Sn,Z/p) -- 3.5.4 The Reduced Norm and a Decomposition of Sn -- 3.5.5 Cohomology in Case n=2 and p>2 -- 3.5.5.1 The Case p>3 -- 3.5.5.2 The Case p=3 -- 3.5.5.3 The Case p=2 -- 3.6 Cohomology with Non-trivial Coefficients and Resolutions -- 3.6.1 The Case n=1 -- 3.6.1.1 The Case p>2 -- 3.6.1.2 The Case p=2 -- 3.6.2 Some Comments on the Case n=2 -- References. |
| Record Nr. | UNINA-9910257380603321 |
| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2017 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||