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Automorphisms of Manifolds and Algebraic $K$-Theory: Part III
 
Michael S. Weiss Mathematisches Institut, Universität Münster, Germany
Bruce E. Williams University of Notre Dame, Indiana
Automorphisms of Manifolds and Algebraic $K$-Theory: Part III
eBook ISBN:  978-1-4704-1720-8
Product Code:  MEMO/231/1084.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
Automorphisms of Manifolds and Algebraic $K$-Theory: Part III
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Automorphisms of Manifolds and Algebraic $K$-Theory: Part III
Michael S. Weiss Mathematisches Institut, Universität Münster, Germany
Bruce E. Williams University of Notre Dame, Indiana
eBook ISBN:  978-1-4704-1720-8
Product Code:  MEMO/231/1084.E
List Price: $71.00
MAA Member Price: $63.90
AMS Member Price: $42.60
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 2312014; 110 pp
    MSC: Primary 57; Secondary 19

    The structure space \(\mathcal{S}(M)\) of a closed topological \(m\)-manifold \(M\) classifies bundles whose fibers are closed \(m\)-manifolds equipped with a homotopy equivalence to \(M\). The authors construct a highly connected map from \(\mathcal{S}(M)\) to a concoction of algebraic \(L\)-theory and algebraic \(K\)-theory spaces associated with \(M\). The construction refines the well-known surgery theoretic analysis of the block structure space of \(M\) in terms of \(L\)-theory.

  • Table of Contents
     
     
    • Chapters
    • 1. Introduction
    • 2. Outline of proof
    • 3. Visible $L$-theory revisited
    • 4. The hyperquadratic $L$–theory of a point
    • 5. Excision and restriction in controlled $L$–theory
    • 6. Control and visible $L$-theory
    • 7. Control, stabilization and change of decoration
    • 8. Spherical fibrations and twisted duality
    • 9. Homotopy invariant characteristics and signatures
    • 10. Excisive characteristics and signatures
    • 11. Algebraic approximations to structure spaces: Set-up
    • 12. Algebraic approximations to structure spaces: Constructions
    • 13. Algebraic models for structure spaces: Proofs
    • A. Homeomorphism groups of some stratified spaces
    • B. Controlled homeomorphism groups
    • C. $K$-theory of pairs and diagrams
    • D. Corrections and Elaborations
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2312014; 110 pp
MSC: Primary 57; Secondary 19

The structure space \(\mathcal{S}(M)\) of a closed topological \(m\)-manifold \(M\) classifies bundles whose fibers are closed \(m\)-manifolds equipped with a homotopy equivalence to \(M\). The authors construct a highly connected map from \(\mathcal{S}(M)\) to a concoction of algebraic \(L\)-theory and algebraic \(K\)-theory spaces associated with \(M\). The construction refines the well-known surgery theoretic analysis of the block structure space of \(M\) in terms of \(L\)-theory.

  • Chapters
  • 1. Introduction
  • 2. Outline of proof
  • 3. Visible $L$-theory revisited
  • 4. The hyperquadratic $L$–theory of a point
  • 5. Excision and restriction in controlled $L$–theory
  • 6. Control and visible $L$-theory
  • 7. Control, stabilization and change of decoration
  • 8. Spherical fibrations and twisted duality
  • 9. Homotopy invariant characteristics and signatures
  • 10. Excisive characteristics and signatures
  • 11. Algebraic approximations to structure spaces: Set-up
  • 12. Algebraic approximations to structure spaces: Constructions
  • 13. Algebraic models for structure spaces: Proofs
  • A. Homeomorphism groups of some stratified spaces
  • B. Controlled homeomorphism groups
  • C. $K$-theory of pairs and diagrams
  • D. Corrections and Elaborations
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.