Cohomology Theories for Compact Abelian Groups [electronic resource] by Karl H. Hofmann, Paul S. Mostert.

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Of all topological algebraic structures compact topological groups have perhaps the richest theory since 80 many different fields contribute to their study: Analysis enters through the representation theory and harmonic analysis; differential geo­ metry, the theory of real analytic functions and the...

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Bibliographic Details
Main Authors: Hofmann, Karl H. (Author)
Mostert, Paul S. (Author)
Corporate Author: SpringerLink (Online service)
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1973.
Edition:1st ed. 1973.
Subjects:
Group theory.
Online Access:
Springer Book Archive - Mathematics: 1973 (Springer Link)
Format: Electronic eBook
Contents:
  • I. Algebraic background
  • Section 1. On exponential functors
  • Section 2. The arithmetic of certain spectral algebras
  • Section 3. Some analogues of the results about spectral algebras with dual derivations
  • Section 4. The Bockstein formalism
  • II. The cohomology of finite abelian groups
  • Section 1. Products
  • Section 2. Special free resolutions for finite abelian groups
  • Section 3. About the cohomology of finite abelian groups in the case of trivial action
  • Section 4. Appendix to Section 3: The low dimensions
  • III. The cohomology of classifying spaces of compact groups
  • Section 1. The functor h
  • Section 2. The functor h for finite groups
  • IV. Kan extensions of functors on dense categories
  • Section 1. Dense categories and continuous functors
  • Section 2. Multiplicative Hopf extensions
  • V. The cohomological structure of compact abelian groups
  • Section 1. The cohomologies of connected compact abelian groups
  • Section 2. The space cohomology of arbitrary compact abelian groups
  • Section 3. The canonical embedding of ? in hG
  • Section 4. Cohomology theories for compact groups over fields as coefficient domains
  • Section 5. The structure of h for arbitrary compact abelian groups and integral coefficients
  • VI. Appendix. Another construction of the functor h
  • Proposition 1. About the graph of < for a topological monoid acting on a space — Proposition 2. Properties of the Dold-Lashof spectrum
  • List of notatio