Spaces of PL Manifolds and Categories of Simple Maps (Am-186) - Waldhausen, Friedhelm; Jahren, Bjørn; Rognes, John
115,99 €
inkl. MwSt.
Versandkostenfrei*
Versandfertig in über 4 Wochen
payback
58 °P sammeln
  • Broschiertes Buch

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…mehr

Andere Kunden interessierten sich auch für
Produktbeschreibung
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. The smooth and topological results then follow by smoothing and triangulation theory. The proof has two main parts. The essence of the first part is a "desingularization," improving arbitrary finite simplicial sets to polyhedra. The second part compares polyhedra with PL manifolds by a thickening procedure. Many of the techniques and results developed should be useful in other connections.
Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Autorenporträt
Friedhelm Waldhausen, Bjørn Jahren & John Rognes