Isotropy groups of homotopy classes of maps
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- by G. Triantafillou
- Trans. Amer. Math. Soc. 334 (1992), 37-48
- DOI: https://doi.org/10.1090/S0002-9947-1992-1044966-8
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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.References
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Bibliographic Information
- © Copyright 1992 American Mathematical Society
- 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