Localization for THH(ku) and the topological Hochschild and cyclic homology of Waldhausen categories /

The authors develop a theory of THH and TC of Waldhausen categories and prove the analogues of Waldhausen's theorems for K-theory. They resolve the longstanding confusion about localization sequences in THH and TC, and establish a specialized dévissage theorem. As applications, the authors pro...

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autores principales: Blumberg, Andrew J. (Autor), Mandell, Michael A. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Providence : American Mathematical Society, [2020].
Colección:Memoirs of the American Mathematical Society ; no. 1286.
Temas:
K-theory.
Algebraic topology.
Cobordism theory.
Homology theory.
K-théorie.
Topologie algébrique.
Théorie des cobordismes.
Homologie.
Topología algebraica
Homología, Teoría de
Cobordismo, Teoría de
Algebraic topology
Cobordism theory
Homology theory
K-theory
$K$-theory [See also 16E20, 18F25] > Higher algebraic $K$-theory > $K$-theory and homology; cyclic homology and cohomology [See also 18G60].
Algebraic topology > Homotopy theory {For simple homotopy type, see 57Q10} > Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.).
$K$-theory [See also 16E20, 18F25] > Topological $K$-theory [See also 55N15, 55R50, 55S25] > Connective $K$-theory, cobordism [See also 55N22].
$K$-theory [See also 16E20, 18F25] > Higher algebraic $K$-theory > Algebraic $K$-theory of spaces.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title page
  • Introduction
  • Chapter 1. Review of , , and
  • 1.1. Review of spectral categories
  • 1.2. Review of the construction of , , and
  • 1.3. Review of the invariance properties of
  • 1.4. The Dennis-Waldhausen Morita Argument
  • Chapter 2. and of simplicially enriched Waldhausen categories
  • 2.1. Simplicially enriched Waldhausen categories
  • 2.2. Spectral categories associated to simplicially enriched Waldhausen categories
  • 2.3. The \Sdot and Moore nerve constructions
  • 2.4. The Moore \Spdot construction
  • 2.5. , , and the cyclotomic trace
  • Chapter 3. -theory theorems in and
  • 3.1. The Additivity Theorem
  • 3.2. The Cofiber Theorem
  • 3.3. The Localization Theorem
  • 3.4. The Sphere Theorem
  • 3.5. Proof of the Sphere Theorem
  • Chapter 4. Localization sequences for and
  • 4.1. The localization sequence for of a discrete valuation ring
  • 4.2. The localization sequence for ( ) and related ring spectra
  • 4.3. Proof of the Dévissage Theorem
  • Chapter 5. Generalization to Waldhausen categories with factorization
  • 5.1. Weakly exact functors
  • 5.2. Embedding in simplicially tensored Waldhausen categories
  • 5.3. Spectral categories and Waldhausen categories
  • Bibliography
  • Index
  • Back Cover.

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