Generators for a complex hyperbolic braid group

Abstract

We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic $13$-space, take the quotient of the remaining space by a discrete group, and find generators for the orbifold fundamental group of the quotient. These generators have the most natural form: loops corresponding to the hyperplanes which come nearest the basepoint. Our results support the conjecture that motivated this study, the "monstrous proposal", which posits a relationship between this braid group and the monster finite simple group.

46 pages, 7 figures, submitted

References in corpus (2)

• Geometric generators for braid-like groups
• Completions, branched covers, Artin groups and singularity theory

Cited by in corpus (2)

• The Deligne-Mostow 9-ball, and the monster
• A new complex reflection group in $PU(9,1)$ and the Barnes-Wall lattice