The complex of partial bases of a free group

Abstract

We prove that the simplicial complex whose simplices are the nonempty partial bases of ${\mathbb{F}}_n$ is homotopy equivalent to a wedge of $(n-1)$-spheres. Moreover, we show that it is Cohen-Macaulay.

Cited by in corpus (3)

• The free factor complex and the dualizing module for the automorphism group of a free group
• Posets arising from decompositions of objects in a monoidal category
• Connectivity of partial basis complexes of freely decomposable groups