Characters of surface groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911643220312064 |
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| author | Gao, David Ioana, Adrian Vigdorovich, Itamar |
| author_facet | Gao, David Ioana, Adrian Vigdorovich, Itamar |
| contents | We initiate the study of characters of surface groups and their corresponding tracial representations. We show that any tracial representation can be approximated arbitrarily well in the Wasserstein topology by factorial tracial representations with spectral gap. In particular, we deduce that the space of traces of a surface group is the Poulsen simplex, thereby resolving positively a question posed by Orovitz, Slutsky, and the third author. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_02242 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Characters of surface groups Gao, David Ioana, Adrian Vigdorovich, Itamar Group Theory Operator Algebras 46L10, 20F65, 22D10, 46L30, 46A55 We initiate the study of characters of surface groups and their corresponding tracial representations. We show that any tracial representation can be approximated arbitrarily well in the Wasserstein topology by factorial tracial representations with spectral gap. In particular, we deduce that the space of traces of a surface group is the Poulsen simplex, thereby resolving positively a question posed by Orovitz, Slutsky, and the third author. |
| title | Characters of surface groups |
| topic | Group Theory Operator Algebras 46L10, 20F65, 22D10, 46L30, 46A55 |
| url | https://arxiv.org/abs/2605.02242 |