Automorphisms of spaces with finite fundamental group

Triantafillou, Georgia

doi:10.1090/S0002-9947-1995-1316864-6

Automorphisms of spaces with finite fundamental group
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Trans. Amer. Math. Soc. 347 (1995), 3391-3403 Request permission

Abstract:

Let $X$ be a finite CW-complex with finite fundamental group. We show that the group ${\text {aut}}(X)$ of homotopy classes of self-homotopy equivalences of $X$ is commensurable to an arithmetic group. If in addition $X$ is an oriented manifold then the subgroup ${\text {au}}{{\text {t}}_t}(X)$ of homotopy classes of tangential homotopy equivalences is commensurable to an arithmetic group. Moreover if $X$ is a smooth manifold of dimension $\geqslant 5$ then the subgroup ${\text {diff}}(X)$ of ${\text {aut}}(X)$ the elements of which are represented by diffeomorphisms is also commensurable to an arithmetic group.

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An algebraic model for

-homotopy types

113-114

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