Geodesic
Dimension functions for spherical fibrations
Okay, Cihan1 ; Yalçin, Ergün2
1 Department of Mathematics, Middlesex College, Western University, London, ON, Canada
2 Department of Mathematics, Bilkent University, Ankara, Turkey
Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 3907-3941

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Given a spherical fibration ξ over the classifying space BG of a finite group G we define a dimension function for the m–fold fiber join of ξ, 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 Qd(p) = (ℤ∕p)2 ⋊ SL2(ℤ∕p) with p–effective Euler class, generalizing a result of Ünlü (2004) about group actions on finite complexes homotopy equivalent to a sphere. We have been informed that this result will also appear in upcoming work of Alejandro Adem and Jesper Grodal as a corollary of a previously announced program on homotopy group actions due to Grodal.

DOI : 10.2140/agt.2018.18.3907
Classification : 55M35, 55S10, 55S37
Keywords: group actions, Smith theory, spherical fibrations, Lannes' $T$–functor

Okay, Cihan 1 ; Yalçin, Ergün 2

1 Department of Mathematics, Middlesex College, Western University, London, ON, Canada
2 Department of Mathematics, Bilkent University, Ankara, Turkey 
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Okay, Cihan; Yalçin, Ergün. Dimension functions for spherical fibrations. Algebraic and Geometric Topology, Tome 18 (2018) no. 7, pp. 3907-3941. doi: 10.2140/agt.2018.18.3907

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