Generators for a complex hyperbolic braid group

Allcock, Daniel¹ ; Basak, Tathagata²

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

Geometry & topology, Tome 22 (2018) no. 6, pp. 3435-3500.

Résumé

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 space. 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.

Détail

DOI : 10.2140/gt.2018.22.3435

Classification : 57M05, 20F36, 32S22, 52C35
Keywords: fundamental group, presentations, Artin groups, braid group, hyperplane arrangements, lattices in PU(1,n), Leech lattice, monster

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