Degenerations of k-positive surface group representations
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866909230706982912 |
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| author | Beyrer, Jonas Pozzetti, Beatrice |
| author_facet | Beyrer, Jonas Pozzetti, Beatrice |
| contents | We introduce \emph{k-positive representations}, a large class of $\{1,\ldots,k\}$--Anosov surface group representations into PGL(E) that share many features with Hitchin representations, and we study their degenerations: unless they are Hitchin, they can be deformed to non-discrete representations, but any limit is at least (k-3)-positive and irreducible limits are (k-1)-positive. A major ingredient, of independent interest, is a general limit theorem for positively ratioed representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_05983 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Degenerations of k-positive surface group representations Beyrer, Jonas Pozzetti, Beatrice Geometric Topology Differential Geometry Group Theory We introduce \emph{k-positive representations}, a large class of $\{1,\ldots,k\}$--Anosov surface group representations into PGL(E) that share many features with Hitchin representations, and we study their degenerations: unless they are Hitchin, they can be deformed to non-discrete representations, but any limit is at least (k-3)-positive and irreducible limits are (k-1)-positive. A major ingredient, of independent interest, is a general limit theorem for positively ratioed representations. |
| title | Degenerations of k-positive surface group representations |
| topic | Geometric Topology Differential Geometry Group Theory |
| url | https://arxiv.org/abs/2106.05983 |