Automorphisms of Manifolds and Algebraic $K$-Theory: Part III

Michael S. Weiss, Bruce E. Williams (Autoren)

Buch | Softcover

110 Seiten

2014
American Mathematical Society (Verlag)
978-1-4704-0981-4 (ISBN)

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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.

Michael S. Weiss, Mathematisches Institut, Universitat Munster, Germany Bruce E. Williams, University of Notre Dame, Indiana, USA

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

Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	400 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-0981-X / 147040981X
ISBN-13	978-1-4704-0981-4 / 9781470409814
Zustand	Neuware