The Deligne–Mostow 9-ball, and the monster

Allcock, Daniel¹ ; Basak, Tathagata²

¹Department of Mathematics, University of Texas at Austin, Austin, TX, United States
²Department of Mathematics, Iowa State University, Ames, IA, United States

Geometry & topology, Tome 29 (2025) no. 2, pp. 791-828

Résumé

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 × M) ⋊ 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 and 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.

Détail

DOI : 10.2140/gt.2025.29.791

Keywords: monster, ball quotient, braid group

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