Compact components of planar surface group representations
| Autor: | William Goldman |
|---|---|
| Rok vydání: | 2023 |
| Zdroj: | Computational Aspects of Discrete Subgroups of Lie Groups. :69-82 |
| ISSN: | 1098-3627 0271-4132 |
| DOI: | 10.1090/conm/783/15701 |
| Popis: | Recently Deroin, Tholozan and Toulisse found connected components of relative character varieties of surface group representations in a Hermitian Lie group G G with remarkable properties. For example, although the Lie groups are never compact, these components are compact. In this way they behave more like relative character varieties for compact Lie groups. (A relative character variety comprises equivalence classes of homomorphisms of the fundamental group of a surface S S , where the holonomy around each boundary component of S S is constrained to a fixed conjugacy class in G G .) The first examples were found by Robert Benedetto and myself in an REU in summer 1992. Here S S is the 4-holed sphere and G = S L ( 2 , R ) G = {\mathsf {SL}}({2,\mathbb {R}}) . Although computer visualization played an important role in the discovery of these unexpected compact components, computation was invisible in the final proof, and its subsequent extensions. |
| Databáze: | OpenAIRE |
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