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# The Wall Invariant of Certain $S^1$ Bundles

Douglas R. Anderson
Proceedings of the American Mathematical Society
Vol. 31, No. 2 (Feb., 1972), pp. 529-535
DOI: 10.2307/2037567
Stable URL: http://www.jstor.org/stable/2037567
Page Count: 7
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## Abstract

Let $p:E \rightarrow B$ be a principal $S^1$ bundle with $B$ dominated by a finite complex. Then it is easy to show that $E$ is also dominated by a finite complex. In this paper we show, under suitable additional hypotheses, that in fact $E$ has the homotopy type of a finite complex. The proof is carried out by computing Wall's finiteness obstruction for $E$.

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