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arXiv · 1702.05707

Generators for a complex hyperbolic braid group

Daniel Allcock·Tathagata Basak
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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.

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Daniel Allcock, Tathagata Basak. 2017-02-19. Generators for a complex hyperbolic braid group. https://doi.org/10.2140/gt.2018.22.3435

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