Equivariant orthogonal spectra and S-modules / M.A. Mandell, J.P. May.

Format:

Book

Author/Creator:

Mandell, M. A., 1970- author.

May, J. Peter, author.

Series:

Memoirs of the American Mathematical Society ; no. 755.

Memoirs of the American Mathematical Society, 0065-9266 ; number 755

Language:

English

Subjects (All):

Homotopy theory.

Categories (Mathematics).

Physical Description:

1 online resource (125 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 2002.

Language Note:

English

Summary:

The previous years have seen a revolution in our understanding of the foundations of stable homotopy theory. Many symmetric monoidal model categories of spectra whose homotopy categories are equivalent to the stable homotopy category are now known, whereas no such categories were known before 1993.

Contents:

""Contents""; ""Introduction""; ""Chapter I. Orthogonal spectra and S-modules""; ""1. Introduction and statements of results""; ""2. Right exact functors on categories of diagram spaces""; ""3. The proofs of the comparison theorems""; ""4. Further Quillen equivalences and homotopical preliminaries""; ""5. Model structures and homotopical proofs""; ""6. The construction of the functor N*""; ""7. The functor M and its comparison with N""; ""8. A revisionist view of infinite loop space theory""; ""Chapter II. Equivariant orthogonal spectra""; ""1. Preliminaries on equivariant categories""

""2. The definition of orthogonal G-spectra""""3. The smash product of orthogonal G-spectra""; ""4. A description of orthogonal G-spectra as diagram G-spaces""; ""Chapter III. Model categories of orthogonal G-spaces""; ""1. The model structure on G-spaces""; ""2. The level model structure on orthogonal G-spectra""; ""3. The homotopy groups of G-prespectra""; ""4. The stable model structure on orthogonal G-spectra""; ""5. The positive stable model structure""; ""6. Stable equivalences of orthogonal G-spectra""; ""7. Model categories of ring and module G-spectra""

""8. The model category of commutative ring G-spectra""""9. Level equivalences and π[sub(*)]-isomorphisms of Ω-G-spectra""; ""Chapter IV. Orthogonal G-spectra and S[sub(G)]-modules""; ""1. Introduction and statements of results""; ""2. Model structures on the category of S[sub(G)]-modules""; ""3. The construction of the functors N and N[sup(#)]""; ""4. The proofs of the comparison theorems""; ""5. The functor M and its comparison with N""; ""6. Families, cofamilies, and Bousfield localization""; ""Chapter V. ""Change"" functors for orthogonal G-spectra""; ""1. Change of universe""

""2. Change of groups""""3. Fixed point and orbit spectra""; ""4. Geometric fixed point spectra""; ""Chapter VI. ""Change"" functors for S[sub(G)]-modules and comparisons""; ""1. Comparisons of change of group functors""; ""2. Comparisons of change of universe functors""; ""3. Comparisons of fixed point and orbit G-spectra functors""; ""4. N-free G-spectra and the Adams isomorphism""; ""5. The geometric fixed point functor and quotient groups""; ""6. Technical results on the unit map λ:JE [omitted] E""; ""Bibliography""; ""Index of Notation""

Notes:

"Volume 159, number 755 (second of 5 numbers)."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-0348-X