The Deligne-Mostow 9-ball, and the monster
Geometric Topology
2025-03-19 v1 Group Theory
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.
Keywords
Cite
@article{arxiv.2309.00148,
title = {The Deligne-Mostow 9-ball, and the monster},
author = {Daniel Allcock and Tathagata Basak},
journal= {arXiv preprint arXiv:2309.00148},
year = {2025}
}