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Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 / / Laurence C. Siebenmann, Robion C. Kirby



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Autore: Kirby Robion C. Visualizza persona
Titolo: Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88 / / Laurence C. Siebenmann, Robion C. Kirby Visualizza cluster
Pubblicazione: Princeton, NJ : , : Princeton University Press, , [2016]
©1977
Descrizione fisica: 1 online resource (373 pages) : illustrations
Disciplina: 514/.7
Soggetto topico: Manifolds (Mathematics)
Piecewise linear topology
Triangulating manifolds
Soggetto non controllato: Affine space
Algebraic topology (object)
Approximation
Associative property
Automorphism
Big O notation
CW complex
Calculation
Cap product
Cartesian product
Category of sets
Chain complex
Classification theorem
Classifying space
Cobordism
Codimension
Cofibration
Cohomology
Connected space
Continuous function (set theory)
Continuous function
Counterexample
Diffeomorphism
Differentiable manifold
Differential structure
Differential topology
Dimension (vector space)
Direct proof
Disjoint union
Elementary proof
Embedding
Euclidean space
Existence theorem
Existential quantification
Fiber bundle
Fibration
General position
Geometry
Group homomorphism
H-cobordism
H-space
Handle decomposition
Handlebody
Hauptvermutung
Hausdorff space
Hilbert cube
Homeomorphism group
Homeomorphism
Homomorphism
Homotopy group
Homotopy
Inclusion map
Injective function
Invertible matrix
K-cell (mathematics)
Kan extension
Linear subspace
Linear topology
Manifold
Mapping cylinder
Mathematical induction
Mathematician
Metric space
Morse theory
Neighbourhood (mathematics)
Open set
Partition of unity
Piecewise linear manifold
Piecewise linear
Poincaré conjecture
Polyhedron
Principal bundle
Product metric
Pushout (category theory)
Regular homotopy
Retract
Sheaf (mathematics)
Simplicial complex
Smoothing
Spin structure
Stability theory
Stable manifold
Standard map
Submanifold
Submersion (mathematics)
Subset
Surgery exact sequence
Surjective function
Theorem
Topological group
Topological manifold
Topological space
Topology
Transversal (geometry)
Transversality (mathematics)
Transversality theorem
Union (set theory)
Uniqueness theorem
Vector bundle
Zorn's lemma
Classificazione: SI 830
Persona (resp. second.): SiebenmannLaurence C.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Frontmatter -- Foreword -- Table of contents -- Guide -- Essay I. Deformation of smooth and piecewise linear manifold structures / Kirby, R. / Siebenmann, L. -- Essay II. Deformation of sliced families of manifold structures / Siebenmann, L. -- Essay III. Some basic theorems about topological manifolds / Siebenmann, L. / Kirby, R. -- Essay IV. Stable classification of smooth and piecewise linear manifold structures / Siebenmann, L. -- Essay V. Classification of sliced families of manifold structures / Siebenmann, L. -- Annex A. Stable homeomorphisms and the annulus conjecture / Kirby, Robion C. -- Annex B. On The Triangulation of Manifolds and the Hauptvermutung / Kirby, R. C. / Siebenmann, L. C. -- Annex C. Topological Manifolds / Siebenmann, L. C. -- Note on Involutions / Atiyah, M. F. -- Combined Bibliography -- Index -- Backmatter
Sommario/riassunto: Since Poincaré's time, topologists have been most concerned with three species of manifold. The most primitive of these--the TOP manifolds--remained rather mysterious until 1968, when Kirby discovered his now famous torus unfurling device. A period of rapid progress with TOP manifolds ensued, including, in 1969, Siebenmann's refutation of the Hauptvermutung and the Triangulation Conjecture. Here is the first connected account of Kirby's and Siebenmann's basic research in this area.The five sections of this book are introduced by three articles by the authors that initially appeared between 1968 and 1970. Appendices provide a full discussion of the classification of homotopy tori, including Casson's unpublished work and a consideration of periodicity in topological surgery.
Titolo autorizzato: Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88), Volume 88  Visualizza cluster
ISBN: 1-4008-8150-1
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910154753803321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; Number 88.