The double coset theorem formula for algebraic K-theory of spaces
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.
scientific article; zbMATH DE number 1786893