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Topological manifold bundles and the $A$-theory assembly map

Raptis, George ; Steimle, Wolfgang


We give a new proof of an index theorem for fiber bundles of compact topological manifolds due to Dwyer, Weiss, and Williams, which asserts that the parametrized A-theory characteristic of such a fiber bundle factors canonically through the assembly map of A-theory. Furthermore our main result shows a refinement of this statement by providing such a factorization for an extended A-theory ...


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