The double coset theorem formula for algebraic K-theory of spaces
type: Item
instance of: scholarly article
title: The double coset theorem formula for algebraic K-theory of spaces
zbMATH Open document ID: 1003.19001
DOI: 10.1023/A:1015654923848
author: Wojciech Dorabiala
published in: \(K\)-Theory
publication date: 2002-08-21T00:00:00Z
review text: The author develops transfers \(p^{\ast}: A(B) \to A(E)\) in Waldhausen's \(A\)-theory of spaces for fibrations \(p: E \to B\) with fibres finitely dominated by finite CW-complexes. He proves an additivity theorem for Williams' parameterized Euler characteristic in the case of fibrations as above which are patched together along cofibrations in the total space. This result leads to a general transfer additivity theorem for such fibrations. If \(G\) is a compact Lie group, the author derives a ``sum theorem'' for \(G\)-bundles with fibre a finite \(G\)-CW-complex; this result is analogous to a formula of Feshbach, and it specializes to a double coset formula. The author proves an additivity result for the homotopy Reidemeister torsion of Dwyer, Weiss and Williams.
Mathematics Subject Classification ID: 19D10
Mathematics Subject Classification ID: 55R12
zbMATH DE Number: 1786893
zbMATH Keywords: A-theory
zbMATH Keywords: transfer
MaRDI profile type: Publication
full work available at URL: a:1015654923848
OpenAlex ID: W2065912997
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description: scientific article; zbMATH DE number 1786893