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Automorphisms of manifolds and algebraic $K$–theory: Part III


About this Title

Michael S. Weiss and Bruce E. Williams

Publication: Memoirs of the American Mathematical Society
Publication Year: 2014; Volume 231, Number 1084
ISBNs: 978-1-4704-0981-4 (print); 978-1-4704-1720-8 (online)
DOI: http://dx.doi.org/10.1090/memo/1084
Published electronically: January 14, 2014

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Outline of proof
  • Chapter 3. Visible $L$-theory revisited
  • Chapter 4. The hyperquadratic $L$–theory of a point
  • Chapter 5. Excision and restriction in controlled $L$–theory
  • Chapter 6. Control and visible $L$-theory
  • Chapter 7. Control, stabilization and change of decoration
  • Chapter 8. Spherical fibrations and twisted duality
  • Chapter 9. Homotopy invariant characteristics and signatures
  • Chapter 10. Excisive characteristics and signatures
  • Chapter 11. Algebraic approximations to structure spaces: Set-up
  • Chapter 12. Algebraic approximations to structure spaces: Constructions
  • Chapter 13. 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

Abstract


The structure space of a closed topological -manifold classifies bundles whose fibers are closed -manifolds equipped with a homotopy equivalence to . We construct a highly connected map from to a concoction of algebraic -theory and algebraic -theory spaces associated with . The construction refines the well-known surgery theoretic analysis of the block structure space of in terms of -theory.

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