eBook ISBN:  9781470417208 
Product Code:  MEMO/231/1084.E 
List Price:  $71.00 
MAA Member Price:  $63.90 
AMS Member Price:  $42.60 
eBook ISBN:  9781470417208 
Product Code:  MEMO/231/1084.E 
List Price:  $71.00 
MAA Member Price:  $63.90 
AMS Member Price:  $42.60 

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 wellknown surgery theoretic analysis of the block structure space of \(M\) in terms of \(L\)theory.

Table of Contents

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: Setup

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


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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 wellknown 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: Setup

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