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

Michael S. Weiss Mathematisches Institut, Universität Münster, Germany
Bruce E. Williams University of Notre Dame, Indiana
Available Formats:
Electronic ISBN: 978-1-4704-1720-8
Product Code: MEMO/231/1084.E
List Price: $71.00 MAA Member Price:$63.90
AMS Member Price: $42.60 Click above image for expanded view Automorphisms of Manifolds and Algebraic$K$-Theory: Part III Michael S. Weiss Mathematisches Institut, Universität Münster, Germany Bruce E. Williams University of Notre Dame, Indiana Available Formats:  Electronic ISBN: 978-1-4704-1720-8 Product Code: MEMO/231/1084.E  List Price:$71.00 MAA Member Price: $63.90 AMS Member Price:$42.60
• Book Details

Memoirs of the American Mathematical Society
Volume: 2312014; 110 pp
MSC: Primary 57; Secondary 19;

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.

• Chapters
• 1. Introduction
• 2. Outline of proof
• 3. Visible $L$-theory revisited
• 4. The hyperquadratic $L$–theory of a point
• 5. Excision and restriction in controlled $L$–theory
• 6. Control and visible $L$-theory
• 7. Control, stabilization and change of decoration
• 8. Spherical fibrations and twisted duality
• 9. Homotopy invariant characteristics and signatures
• 10. Excisive characteristics and signatures
• 11. Algebraic approximations to structure spaces: Set-up
• 12. Algebraic approximations to structure spaces: Constructions
• 13. Algebraic models for structure spaces: Proofs
• A. Homeomorphism groups of some stratified spaces
• B. Controlled homeomorphism groups
• C. $K$-theory of pairs and diagrams
• D. Corrections and Elaborations
• Requests

Review Copy – for reviewers who would like to review an AMS book
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Volume: 2312014; 110 pp
MSC: Primary 57; Secondary 19;

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.

• Chapters
• 1. Introduction
• 2. Outline of proof
• 3. Visible $L$-theory revisited
• 4. The hyperquadratic $L$–theory of a point
• 5. Excision and restriction in controlled $L$–theory
• 6. Control and visible $L$-theory
• 7. Control, stabilization and change of decoration
• 8. Spherical fibrations and twisted duality
• 9. Homotopy invariant characteristics and signatures
• 10. Excisive characteristics and signatures
• 11. Algebraic approximations to structure spaces: Set-up
• 12. Algebraic approximations to structure spaces: Constructions
• 13. Algebraic models for structure spaces: Proofs
• A. Homeomorphism groups of some stratified spaces
• B. Controlled homeomorphism groups
• C. $K$-theory of pairs and diagrams
• D. Corrections and Elaborations
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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