Algebraic & Geometric Topology

Dimension functions for spherical fibrations

Cihan Okay and Ergün Yalçin

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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 ) = ( p ) 2 SL 2 ( 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
Received: 30 October 2017
Revised: 1 June 2018
Accepted: 11 June 2018
First available in Project Euclid: 18 December 2018

Permanent link to this document
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

Subjects
Primary: 55M35: Finite groups of transformations (including Smith theory) [See also 57S17]
Secondary: 55S10: Steenrod algebra 55S37: Classification of mappings

Keywords
group actions Smith theory spherical fibrations Lannes' $T$–functor

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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