Spaces of PL manifolds and categories of simple maps /
Waldhausen, Friedhelm, 1938-
Spaces of PL manifolds and categories of simple maps / Friedhelm Waldhausen, Bjørn Jahren, and John Rognes. - Princeton : Princeton University Press, 2013. - 1 online resource - Annals of mathematics studies ; no. 186 . - Annals of mathematics studies ; no. 186. .
Includes bibliographical references and index.
Frontmatter -- Contents -- Introduction -- 1. The stable parametrized h-cobordism theorem -- 2. On simple maps -- 3. The non-manifold part -- 4. The manifold part -- Bibliography -- Symbols -- Index.
Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing Waldhausen's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract.
In English.
9781400846528 (electronic bk.) 1400846528 (electronic bk.)
10.1515/9781400846528 doi
22573/ctt22nt7c JSTOR
Piecewise linear topology.
Mappings (Mathematics)
Topologie linéaire par morceaux.
Applications (Mathématiques)
MATHEMATICS--Topology.
MATHEMATICS--Transformations.
Mappings (Mathematics)
Piecewise linear topology.
Electronic books.
Electronic books.
QA613.4 / .W35 2013eb
514/.22
Spaces of PL manifolds and categories of simple maps / Friedhelm Waldhausen, Bjørn Jahren, and John Rognes. - Princeton : Princeton University Press, 2013. - 1 online resource - Annals of mathematics studies ; no. 186 . - Annals of mathematics studies ; no. 186. .
Includes bibliographical references and index.
Frontmatter -- Contents -- Introduction -- 1. The stable parametrized h-cobordism theorem -- 2. On simple maps -- 3. The non-manifold part -- 4. The manifold part -- Bibliography -- Symbols -- Index.
Since its introduction by Friedhelm Waldhausen in the 1970s, the algebraic K-theory of spaces has been recognized as the main tool for studying parametrized phenomena in the theory of manifolds. However, a full proof of the equivalence relating the two areas has not appeared until now. This book presents such a proof, essentially completing Waldhausen's program from more than thirty years ago. The main result is a stable parametrized h-cobordism theorem, derived from a homotopy equivalence between a space of PL h-cobordisms on a space X and the classifying space of a category of simple maps of spaces having X as deformation retract.
In English.
9781400846528 (electronic bk.) 1400846528 (electronic bk.)
10.1515/9781400846528 doi
22573/ctt22nt7c JSTOR
Piecewise linear topology.
Mappings (Mathematics)
Topologie linéaire par morceaux.
Applications (Mathématiques)
MATHEMATICS--Topology.
MATHEMATICS--Transformations.
Mappings (Mathematics)
Piecewise linear topology.
Electronic books.
Electronic books.
QA613.4 / .W35 2013eb
514/.22