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- W2283362129 abstract "We raise the question of realizability of group actions which is an extended version of the 1960's Kahn realizability problem for (abstract) groups. Namely, if $M$ is a $mathbb ZG$-module for a group $G$, we say that a simply-connected space $X$ realize this action if, for some $k$, $pi_k(X)$ as a $mathbb Z mathcal E (X) $-module for the group $mathcal E (X)$ of self-homotopy equivalences of $X$, is isomorphic to $M$ as a $mathbb ZG$-module. Which modules can be so realized? In this paper we obtain a positive answer for any faithful finitely generated $mathbb Q G$-module, where $G$ is finite. Our proof relies on providing a positive answer to Kahn's problem for a large class of orthogonal groups of which, by using invariant theory, our case is shown to be a particular one." @default.
- W2283362129 created "2016-06-24" @default.
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- W2283362129 date "2015-11-19" @default.
- W2283362129 modified "2023-10-01" @default.
- W2283362129 title "On the realizability of group actions" @default.
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