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The
Deligne–Mostow $9$-ball, and the monster
Daniel Allcock and Tathagata Basak |
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Geometry & Topology 29 (2025) 791–828
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Abstract |
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The “monstrous proposal” of the first author is that the quotient of a certain -dimensional complex hyperbolic braid group, by the relations that its natural generators have order , is the “bimonster” . Here is the monster simple group. We prove that this quotient is either the bimonster or . In the process, we give new information about the isomorphism, found by Deligne and Mostow, between the moduli space of -tuples in and a quotient of the complex -ball. Namely, we identify which loops in the -ball quotient correspond to the standard braid generators. |
Keywords
monster, ball quotient, braid group
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Mathematical Subject Classification
Primary: 20F36, 22E40
Secondary: 20D08
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References |
Publication
Received: 31 August 2023
Revised: 25 March 2024
Accepted: 4 May 2024
Published: 12 March 2025
Proposed: Benson Farb
Seconded: David Fisher, Mladen Bestvina
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Authors |
| Daniel Allcock | |
| Department of Mathematics University of Texas at Austin Austin, TX United States |
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| http://www.math.utexas.edu/~allcock | |
| Tathagata Basak | |
| Department of Mathematics Iowa State University Ames, IA United States |
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| https://orion.math.iastate.edu/tathagat/ | |
| © 2025 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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