Automorphisms of Manifolds and Algebraic $K$-Theory: Part III
Published on 30. August 2014
Book
Paperback/Softback
110 pages
978-1-4704-0981-4 (ISBN)
Description
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.
More details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
Dimensions
Height: 254 mm
Width: 178 mm
Weight
400 gr
ISBN-13
978-1-4704-0981-4 (9781470409814)
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Schweitzer Classification
Persons
Michael S. Weiss, Mathematisches Institut, Universitat Munster, Germany
Bruce E. Williams, University of Notre Dame, Indiana, USA
Bruce E. Williams, University of Notre Dame, Indiana, USA
Content
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