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arXiv · 2309.00148

The Deligne-Mostow 9-ball, and the monster

Daniel Allcock·Tathagata Basak
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Abstract

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.

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Daniel Allcock, Tathagata Basak. 2023-08-31. The Deligne-Mostow 9-ball, and the monster. https://doi.org/10.2140/gt.2025.29.791

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