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Automorphisms of Manifolds and Algebraic \(K\)-Theory: Part III
Michael S. Weiss, Mathematisches Institut, Universität Münster, Germany, and Bruce E. Williams, University of Notre Dame, Indiana

Memoirs of the American Mathematical Society
2014; 110 pp; softcover
Volume: 231
ISBN-10: 1-4704-0981-X
ISBN-13: 978-1-4704-0981-4
List Price: US$71
Individual Members: US$42.60
Institutional Members: US$56.80
Order Code: MEMO/231/1084
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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

  • Introduction
  • Outline of proof
  • Visible \(L\)-theory revisited
  • The hyperquadratic \(L\)-theory of a point
  • Excision and restriction in controlled \(L\)-theory
  • Control and visible \(L\)-theory
  • Control, stabilization and change of decoration
  • Spherical fibrations and twisted duality
  • Homotopy invariant characteristics and signatures
  • Excisive characteristics and signatures
  • Algebraic approximations to structure spaces: Set-up
  • Algebraic approximations to structure spaces: Constructions
  • Algebraic models for structure spaces: Proofs
  • Appendix A. Homeomorphism groups of some stratified spaces
  • Appendix B. Controlled homeomorphism groups
  • Appendix C. \(K\)-theory of pairs and diagrams
  • Appendix D. Corrections and elaborations
  • Bibliography
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