On the Wall finiteness obstruction for the total space of certain fibrations

Munkholm, Hans J.; Pedersen, Erik Kjaer

doi:10.1090/S0002-9947-1980-0580901-6

On the Wall finiteness obstruction for the total space of certain fibrations
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by Hans J. Munkholm and Erik Kjaer Pedersen

Trans. Amer. Math. Soc. 261 (1980), 529-545

DOI: https://doi.org/10.1090/S0002-9947-1980-0580901-6

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Abstract:

The problem of computing the Wall finiteness obstruction for the total space of a fibration $p: E \to B$ in terms of that for the base and homological data of the fiber has been considered by D. R. Anderson and by E. K. Pedersen and L. R. Taylor. We generalize their results and show how the problem is related to the algebraically defined transfer map ${\varphi ^{\ast }}: {K_0}({\textbf {Z}}{\pi _1}(B)) \to {K_0}({\textbf {Z}}{\pi _1}(E))$, $\varphi = {p_{\ast }}: {\pi _1}(E) \to {\pi _1}(B)$, whenever the latter is defined.

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