Uniqueness theorem for completely non-degenerate B-groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866911252579614720 |
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| author | Glutsyuk, A. A. Ilyashenko, Yu. S. |
| author_facet | Glutsyuk, A. A. Ilyashenko, Yu. S. |
| contents | We prove that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate B-groups. We also study the factor of a B-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of maps of the first to the second one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_19685 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness theorem for completely non-degenerate B-groups Glutsyuk, A. A. Ilyashenko, Yu. S. Complex Variables Group Theory 30F40 We prove that a completely non-degenerate B-group is uniquely determined by its factor: two such groups with conformally equivalent factors are Möbius conjugate. A similar property is inherent to the quasi-Fuchsian groups but not to degenerate B-groups. We also study the factor of a B-group as a triple: the main factor, the marked characteristic complex, and a homotopy class of maps of the first to the second one. |
| title | Uniqueness theorem for completely non-degenerate B-groups |
| topic | Complex Variables Group Theory 30F40 |
| url | https://arxiv.org/abs/2502.19685 |