Geometric components of representation spaces via robust families of submanifolds
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909745503272960 |
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| author | Viaggi, Gabriele |
| author_facet | Viaggi, Gabriele |
| contents | 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 ${\rm Hom}(Γ,G)$. 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 Teichmüller 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 ${\rm Hom}(Γ,G)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_14842 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric components of representation spaces via robust families of submanifolds Viaggi, Gabriele Geometric Topology Group Theory 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 ${\rm Hom}(Γ,G)$. 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 Teichmüller 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 ${\rm Hom}(Γ,G)$. |
| title | Geometric components of representation spaces via robust families of submanifolds |
| topic | Geometric Topology Group Theory |
| url | https://arxiv.org/abs/2508.14842 |