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- W2766957533 abstract "Given a spherical fibration $xi$ over the classifying space $BG$ of a finite group we define a dimension function for the $m-$fold fiber join of $xi$ where $m$ is some large positive integer. We show that the dimension functions satisfy the Borel-Smith conditions when $m$ is large enough. As an application we prove that there exists no spherical fibration over the classifying space of $text{Qd}(p)= (mathbb{Z}/p)^2rtimestext{SL}_2(mathbb{Z}/p)$ with $p-$effective Euler class, generalizing the result of Ozgun Unlu about group actions on finite complexes homotopy equivalent to a sphere. We have been informed that this result will also appear in a future paper as a corollary of a previously announced program on homotopy group actions due to Jesper Grodal." @default.
- W2766957533 created "2017-11-10" @default.
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- W2766957533 date "2018-12-11" @default.
- W2766957533 modified "2023-09-26" @default.
- W2766957533 title "Dimension functions for spherical fibrations" @default.
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- W2766957533 doi "https://doi.org/10.2140/agt.2018.18.3907" @default.
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