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


Authors: Hans J. Munkholm and Erik Kjaer Pedersen
Journal: Trans. Amer. Math. Soc. 261 (1980), 529-545
MSC: Primary 55R05
DOI: https://doi.org/10.1090/S0002-9947-1980-0580901-6
MathSciNet review: 580901
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1980-0580901-6
Keywords: Finiteness obstruction, fibration, transfer map, algebraic K-theory, realizability of torus fibrations
Article copyright: © Copyright 1980 American Mathematical Society

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