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Generators for a complex
hyperbolic braid group
Daniel Allcock and Tathagata Basak |
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Geometry & Topology 22 (2018) 3435–3500
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Abstract |
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We give generators for a certain complex hyperbolic braid group. That is, we remove a hyperplane arrangement from complex hyperbolic –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. |
Keywords
fundamental group, presentations, Artin groups, braid
group, hyperplane arrangements, lattices in PU(1,n), Leech
lattice, monster
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Mathematical Subject Classification 2010
Primary: 57M05
Secondary: 20F36, 32S22, 52C35
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References |
Publication
Received: 18 February 2017
Revised: 14 September 2017
Accepted: 20 November 2017
Published: 23 September 2018
Proposed: Walter Neumann
Seconded: Anna Wienhard, Benson Farb
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Authors |
| Daniel Allcock | |
| Department of Mathematics University of Texas at Austin Austin, TX United States |
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| http://www.math.utexas.edu/~allcock | |
| Tathagata Basak | |
| Department of Mathematics Iowa State University Ames, IA United States |
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| http://orion.math.iastate.edu/tathagat | |
