Spaces of PL manifolds and categories of simple maps / Friedhelm Waldhausen, Bjørn Jahren, and John Rognes.

Format:

Book

Author/Creator:

Waldhausen, Friedhelm, 1938-

Contributor:

Jahren, Bjørn, 1945-

Rognes, John.

Series:

Annals of mathematics studies ; no. 186.

Annals of mathematics studies ; number 186

Language:

English

Subjects (All):

Piecewise linear topology.

Cobordism theory.

Mappings (Mathematics).

Physical Description:

184 pages ; 24 cm.

Place of Publication:

Princeton : Princeton University Press, 2013.

Summary:

Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition into the twenty-first century as Princeton looks forward to publishing the major works of the new millennium. To mark the continued success of the series, all books are again available in paperback. For a complete list of titles, please visit the Princeton University Press Web site: press.princeton.edu. The most recently published volumes include: Book jacket.

Contents:

1 The stable parametrized h-cobordism theorem 7

1.1 The manifold part 7

1.2 The non-manifold part 13

1.3 Algebraic K-theory of spaces 15

1.4 Relation to other literature 20

2 On simple maps 29

2.1 Simple maps of simplicial sets 29

2.2 Normal subdivision of simplicial sets 34

2.3 Geometric realization and subdivision 42

2.4 The reduced mapping cylinder 56

2.5 Making simplicial sets non-singular 68

2.6 The approximate lifting property 74

2.7 Subdivision of simplicial sets over Δ^q 83

3 The non-manifold part 99

3.1 Categories of simple maps 99

3.2 Filling horns 108

3.3 Some homotopy fiber sequences 119

3.4 Polyhedral realization 126

3.5 Tuning Serre fibrations into bundles 131

3.6 Quillen's Theorems A and B 134

4 The manifold part 139

4.1 Spaces of PL manifolds 139

4.2 Spaces of thickenings 150

4.3 Straightening the thickenings 155.

Notes:

Includes bibliographical references (pages 175-178) and index.

ISBN:

9780691157757

0691157758

9780691157764

0691157766

OCLC:

820123500