Current browse context:
math.GR
Change to browse by:
References & Citations
Mathematics > Group Theory
Title: The quasi-isometry invariance of the Coset Intersection Complex
(Submitted on 25 Apr 2024)
Abstract: For a pair $(G,\mathcal{P})$ consisting of a finitely generated group and finite collection of subgroups, we introduce a simplicial $G$-complex $\mathcal{K}(G,\mathcal{P})$ called the coset intersection complex. We prove that the quasi-isometry type and the homotopy type of $\mathcal{K}(G,\mathcal{P})$ are quasi-isometric invariants of the group pair $(G,\mathcal{P})$. Classical properties of $\mathcal{P}$ in $G$ correspond to topological or geometric properties of $\mathcal{K}(G,\mathcal{P})$, such as having finite height, having finite width, being almost malnormal, admiting a malnormal core, or having thickness of order one. As applications, we obtain that a number of algebraic properties of $\mathcal{P}$ in $G$ are quasi-isometry invariants of the pair $(G,\mathcal{P})$. For a certain class of right-angled Artin groups and their maximal parabolic subgroups, we show that the complex $\mathcal{K}(G,\mathcal{P})$ is quasi-isometric to the Deligne complex; in particular, it is hyperbolic.
Submission history
From: Eduardo Martinez-Pedroza [view email][v1] Thu, 25 Apr 2024 14:11:45 GMT (59kb,D)
Link back to: arXiv, form interface, contact.