Spaces of Pl Manifolds and Categories of Simple Maps

Zusatztext "It is a welcome event, after 35 years, to have available a complete proof of Waldhausen's program." ---Bruce Hughes, Zentralblatt MATH Informationen zum Autor Friedhelm Waldhausen, Bjørn Jahren & John Rognes Klappentext 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. Zusammenfassung 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 Waldhau

Product details

• Authors: Phillip Griffiths, Bjorn Jahren, Bjørn Jahren, Bjrn Jahren, John Rognes, Rognes John, Friedhelm Waldhausen, Friedhelm Jahren Waldhausen
• Assisted by: John N. Mather (Editor), Elias Stein (Editor)
• Publisher: Princeton University Press
• Languages: English
• Product format: Paperback / Softback
• Released: 28.04.2013
• EAN: 9780691157764
• ISBN: 978-0-691-15776-4
• No. of pages: 192
• Series: Annals of Mathematics Studies; Annals of Mathematics Studies
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Analysis; MATHEMATICS / Functional Analysis, MATHEMATICS / Topology, Topology, Functional analysis & transforms, Functional analysis and transforms