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arXiv · 1608.01685

Spherical posets from commuting elements

Cihan Okay
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Abstract

In this paper we study the homotopy type of the partially ordered set of left cosets of abelian subgroups in an extraspecial $p$-group. We prove that the universal cover of its nerve is homotopy equivalent to a wedge of $r$-spheres where $2r \geq 4$ is the rank of its Frattini quotient. This determines the homotopy type of the universal cover of the classifying space of transitionally commutative bundles.

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Cihan Okay. 2016-08-04. Spherical posets from commuting elements. https://doi.org/10.1515/jgth-2018-0008

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