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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Isotropy groups of homotopy classes of maps


Author: G. Triantafillou
Journal: Trans. Amer. Math. Soc. 334 (1992), 37-48
MSC: Primary 55S37; Secondary 55P62
DOI: https://doi.org/10.1090/S0002-9947-1992-1044966-8
MathSciNet review: 1044966
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Abstract: Let $ \operatorname{aut}(X)$ be the group of homotopy classes of self-homotopy equivalences of a space $ X$ and let $ [f] \in [X,Y]$ be a homotopy class of maps from $ X$ to $ Y$ . The aim of this paper is to prove that under certain nilpotency and finiteness conditions the isotropy group $ \operatorname{aut}{(X)_{[f]}}$ of $ [f]$ under the action of $ \operatorname{aut}(X)$ on $ [X,Y]$ is commensurable to an arithmetic group. Therefore $ \operatorname{aut}{(X)_{[f]}}$ is a finitely presented group by a result of Borel and Harish-Chandra.


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DOI: https://doi.org/10.1090/S0002-9947-1992-1044966-8
Keywords: Homotopy self-homotopy equivalence, arithmetic group, minimal model
Article copyright: © Copyright 1992 American Mathematical Society

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