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Handbook of homotopy theory /

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The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to wo...

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Bibliographic Details
Corporate Author: Taylor & Francis
Other Authors: Miller, Haynes R., 1948-
Format: eBook
Language:English
Published: [Boca Raton, Florida] : [CRC Press], [2019]
Subjects:
Homotopy theory.
MATHEMATICS / General
MATHEMATICS / Geometry / General
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover
  • Half Title
  • Series Page
  • Title Page
  • Copyright Page
  • Contents
  • Preface
  • 1. Goodwillie calculus
  • 1.1 Polynomial Approximation and the Taylor Tower
  • 1.2 The Classification of Homogeneous Functors
  • 1.3 The Taylor tower of the identity functor for based spaces
  • 1.4 Operads and Tate data: the Classification of Taylor towers
  • 1.5 Applications and calculations in algebraic K-theory
  • 1.6 Taylor towers of infinity-categories
  • 1.7 The manifold and orthogonal calculi
  • 1.8 Further directions
  • Bibliography
  • 2. A factorization homology primer
  • 2.1 Introduction
  • 2.2 Manifolds with tangential structure
  • 2.2.1 Manifolds and embeddings
  • 2.2.2 Sheaves on n-manifolds
  • 2.2.3 Tangent classifier
  • 2.2.4 B-framed manifolds
  • 2.2.5 Examples and discussion of B-framings
  • 2.2.6 Weiss sheaves on n-manifolds
  • 2.2.7 Disks
  • 2.2.8 Manifolds with boundary
  • 2.2.9 Localizing with respect to isotopy equivalences
  • 2.3 Homology theories for manifolds
  • 2.3.1 Disk algebras
  • 2.3.2 Factorization algebras
  • 2.3.3 Factorization homology over oriented 1-manifolds with boundary
  • 2.3.4 Homology theories: definition
  • 2.3.5 Pushforward
  • 2.3.6 Homology theories: characterization
  • 2.4 Nonabelian PoincarĂ© duality
  • 2.5 Calculations
  • 2.5.1 Factorization homology for direct sum
  • 2.5.2 Factorization homology with coefficients in commutative algebras
  • 2.5.3 Factorization homology from Lie algebras
  • 2.5.4 Factorization homology of free DiskBn-algebras
  • 2.6 Filtrations
  • 2.6.1 Cardinality filtrations
  • 2.6.2 Goodwillie filtrations
  • 2.7 PoincarĂ©/Koszul duality
  • 2.8 Factorization homology for singular manifolds
  • 2.8.1 Singular manifolds
  • 2.8.2 Homology theories for structured singular manifolds
  • 2.8.3 Characterizing some Disk(DU)-algebras
  • Bibliography
  • 3. Polyhedral products and features of their homotopy theory
  • 3.1 Introduction
  • 3.2 The origin of polyhedral products in toric topology
  • 3.3 The introduction of moment-angle complexes
  • 3.4 Moment-angle complexes as intersections of quadrics
  • 3.5 The cohomology of moment-angle complexes
  • 3.6 The exponentiation property of polyhedral products
  • 3.7 Fibrations
  • 3.8 Unstable and stable decompositions of the polyhedral product
  • 3.9 Equivariance of the stable splitting and an application to number theory
  • 3.10 The case that Ai = ? for all i
  • 3.11 The cohomology of polyhedral products and a spectral sequence
  • 3.12 A geometric approach to the cohomology of polyhedral products
  • 3.13 Polyhedral products and the Golodness of monomial ideal rings
  • 3.14 Higher Whitehead products and loop spaces
  • Bibliography
  • 4. A guide to tensor-triangular classification
  • 4.1 Introduction
  • 4.2 The tt-spectrum and the classification of tt-ideals
  • 4.3 Topology
  • 4.4 Commutative algebra and algebraic geometry
  • 4.5 Modular representation theory and related topics