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# memo_has_moved_text();Automorphisms of manifolds and algebraic $K$–theory: Part III

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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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 $\mathcal {S}(M)$ of a closed topological $m$-manifold $M$ classifies bundles whose fibers are closed $m$-manifolds equipped with a homotopy equivalence to $M$. We 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.