The Deligne-Mostow 9-ball, and the monster
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866917959577894912 |
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| author | Allcock, Daniel Basak, Tathagata |
| author_facet | Allcock, Daniel Basak, Tathagata |
| contents | The "monstrous proposal" of the first author is that the quotient of a certain 13-dimensional complex hyperbolic braid group, by the relations that its natural generators have order 2, is the bimonster" (M x M)semidirect Z/2. Here M is the monster simple group. We prove that this quotient is either the bimonster or Z/2. In the process, we give new information about the isomorphism found by Deligne-Mostow, between the moduli space of 12-tuples in CP1 and a quotient of the complex 9-ball. Namely, we identify which loops in the 9-ball quotient correspond to the standard braid generators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_00148 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Deligne-Mostow 9-ball, and the monster Allcock, Daniel Basak, Tathagata Geometric Topology Group Theory Primary: 20F36, 22E40, Secondary: 20D08 The "monstrous proposal" of the first author is that the quotient of a certain 13-dimensional complex hyperbolic braid group, by the relations that its natural generators have order 2, is the bimonster" (M x M)semidirect Z/2. Here M is the monster simple group. We prove that this quotient is either the bimonster or Z/2. In the process, we give new information about the isomorphism found by Deligne-Mostow, between the moduli space of 12-tuples in CP1 and a quotient of the complex 9-ball. Namely, we identify which loops in the 9-ball quotient correspond to the standard braid generators. |
| title | The Deligne-Mostow 9-ball, and the monster |
| topic | Geometric Topology Group Theory Primary: 20F36, 22E40, Secondary: 20D08 |
| url | https://arxiv.org/abs/2309.00148 |