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Transactions of the American Mathematical Society

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Automorphisms of spaces with finite fundamental group


Author: Georgia Triantafillou
Journal: Trans. Amer. Math. Soc. 347 (1995), 3391-3403
MSC: Primary 55P62; Secondary 57S99
DOI: https://doi.org/10.1090/S0002-9947-1995-1316864-6
MathSciNet review: 1316864
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1995-1316864-6
Keywords: Homotopy equivalence, diffeomorphism, arithmetic group, minimal model
Article copyright: © Copyright 1995 American Mathematical Society

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