On the dimension of infinite covers

Dwyer, W.; Stolz, S.; Taylor, L.

doi:10.1090/S0002-9939-96-03250-9

On the dimension of infinite covers
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by W. G. Dwyer, S. Stolz and L. R. Taylor PDF

Proc. Amer. Math. Soc. 124 (1996), 2235-2239 Request permission

Abstract:

We prove the following theorem and some generalizations.

Theorem. Let $X$ be a connected CW complex which satisfies Poincaré duality of dimension $n\ge 4$. For any subgroup $H$ of $\pi _1(X)$, let $X_H$ denote the cover of $X$ corresponding to $H$. If $H$ has infinite index in $\pi _1(X)$, then $X_H$ is homotopy equivalent to an $(n-1)$-dimensional CW complex.

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