Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
131 tokens/sec
GPT-4o
10 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Combination theorems in convex projective geometry (2407.09439v2)

Published 12 Jul 2024 in math.GR and math.GT

Abstract: We prove a general combination theorem for discrete subgroups of $\mathrm{PGL}(n,\mathbb{R})$ preserving properly convex open subsets in the projective space $\mathbb{P}(\mathbb{R}n)$, in the spirit of Klein and Maskit. We use it in particular to prove that a free product of two $(\mathbb{Z}$-)linear groups is again ($\mathbb{Z}$-)linear, and to construct Zariski-dense discrete subgroups of $\mathrm{PGL}(n,\mathbb{R})$ which are not lattices but contain a lattice of a smaller higher-rank simple Lie group. We also establish a version of our combination theorem for discrete groups that are convex cocompact in $\mathbb{P}(\mathbb{R}n)$ in the sense of arXiv:1704.08711. In particular, we prove that a free product of two convex cocompact groups is convex cocompact, which implies that the free product of two Anosov groups is Anosov. We also prove a virtual amalgamation theorem over convex cocompact subgroups generalizing work of Baker-Cooper.

Citations (1)

Summary

We haven't generated a summary for this paper yet.