eBook 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 |
eBook 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 |
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 231; 2014; 110 ppMSC: 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.
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Table of Contents
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Chapters
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1. Introduction
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2. Outline of proof
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3. Visible $L$-theory revisited
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4. The hyperquadratic $L$–theory of a point
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5. Excision and restriction in controlled $L$–theory
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6. Control and visible $L$-theory
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7. Control, stabilization and change of decoration
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8. Spherical fibrations and twisted duality
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9. Homotopy invariant characteristics and signatures
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10. Excisive characteristics and signatures
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11. Algebraic approximations to structure spaces: Set-up
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12. Algebraic approximations to structure spaces: Constructions
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13. Algebraic models for structure spaces: Proofs
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A. Homeomorphism groups of some stratified spaces
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B. Controlled homeomorphism groups
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C. $K$-theory of pairs and diagrams
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D. Corrections and Elaborations
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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.
-
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