| Description |
1 online resource (v, 112 pages) |
| Series |
Memoirs of the American Mathematical Society Ser. ; no. 1286 |
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Memoirs of the American Mathematical Society ; no. 1286.
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| Contents |
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 -- |
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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 -- |
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5.2. Embedding in simplicially tensored Waldhausen categories -- 5.3. Spectral categories and Waldhausen categories -- Bibliography -- Index -- Back Cover |
| Summary |
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 prove conjectures of Hesselholt and Ausoni-Rognes about localization cofiber sequences surrounding THH(ku), and more generally establish a framework for advancing the Rognes program for studying Waldhausen's chromatic filtration on A(*) |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Description based upon print version of record |
| Subject |
K-theory.
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Algebraic topology.
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Cobordism theory.
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Homology theory.
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Topología algebraica
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Homología, Teoría de
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Cobordismo, Teoría de
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Algebraic topology
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Homology theory
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K-theory
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Cobordism theory
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$K$-theory [See also 16E20, 18F25] -- Higher algebraic $K$-theory -- $K$-theory and homology; cyclic homology and cohomology [See also 18G60].
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Algebraic topology -- Homotopy theory {For simple homotopy type, see 57Q10} -- Spectra with additional structure ($E_\infty$, $A_\infty$, ring spectra, etc.).
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$K$-theory [See also 16E20, 18F25] -- Topological $K$-theory [See also 55N15, 55R50, 55S25] -- Connective $K$-theory, cobordism [See also 55N22].
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$K$-theory [See also 16E20, 18F25] -- Higher algebraic $K$-theory -- Algebraic $K$-theory of spaces.
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| Form |
Electronic book
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| Author |
Mandell, Michael A., author
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| ISBN |
1470461404 |
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9781470461409 |
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