Algebraic & Geometric Topology

Dimension functions for spherical fibrations

Abstract

Given a spherical fibration $ξ$ over the classifying space $B G$ 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 $Qd ( p ) = ( ℤ ∕ p ) 2 ⋊ SL 2 ( ℤ ∕ p )$ 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.

Article information

Source
Algebr. Geom. Topol., Volume 18, Number 7 (2018), 3907-3941.

Dates
Revised: 1 June 2018
Accepted: 11 June 2018
First available in Project Euclid: 18 December 2018

https://projecteuclid.org/euclid.agt/1545102058

Digital Object Identifier
doi:10.2140/agt.2018.18.3907

Mathematical Reviews number (MathSciNet)
MR3892235

Zentralblatt MATH identifier
07006381

Citation

Okay, Cihan; Yalçin, Ergün. Dimension functions for spherical fibrations. Algebr. Geom. Topol. 18 (2018), no. 7, 3907--3941. doi:10.2140/agt.2018.18.3907. https://projecteuclid.org/euclid.agt/1545102058

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