Geometric components of representation spaces via robust families of submanifolds

Gabriele Viaggi

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arXiv · 2508.14842

Geometric components of representation spaces via robust families of submanifolds

Gabriele Viaggi

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Abstract

We introduce robust families of submanifolds for a linear Lie group $G$. We show that they give rise to geometric subspaces of the representation space ${\rm Hom}(\Gamma,G)$. As an application, we give a unified short proof of results of Beyrer and Kassel and of Benoist and Koszul about the existence of higher Teichm\"uller components for $G={\rm SO}(p,q+1),{\rm SL}(p+1,\mathbb{R})$. Being based on very general principles, our approach might be suited for finding geometric components in various ${\rm Hom}(\Gamma,G)$.

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Gabriele Viaggi. 2025-08-20. Geometric components of representation spaces via robust families of submanifolds. https://arxiv.org/abs/2508.14842

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