Spherical posets from commuting elements

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 $2r\ge 4$ is the rank of its Frattini quotient. This determines the homotopy type of the universal cover of the classifying space of transitionally commutative bundles.

References in corpus (3)

• A classifying space for commutativity in Lie groups
• Colimits of abelian groups
• Homotopy colimits of classifying spaces of abelian subgroups of a finite group

Cited by in corpus (4)

• On the mod-$\ell$ homology of the classifying space for commutativity
• Higher generation by abelian subgroups in Lie groups
• Classifying space for quantum contextuality
• Commutative d-Torsion K-Theory and Its Applications