The Burau representation and shapes of polyhedra

DOI10.2140/AGT.2024.24.2787MaRDI QIDQ6614588

Ethan Dlugie

Publication date: 7 October 2024

Published in: Algebraic \& Geometric Topology (Search for Journal in Brave)

zbMATH Keywords

braid groupsflat surfacesroots of unityBurau representationshapes of polyhedra

Mathematics Subject Classification ID

Braid groups; Artin groups (20F36) Topology and geometry of orbifolds (57R18) 2-dimensional topology (including mapping class groups of surfaces, Teichmüller theory, curve complexes, etc.) (57K20)

Cites Work

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• Monodromy of cyclic coverings of the projective line
• A presentation for the image of Burau\((4)\otimes Z_2\)
• Three-dimensional orbifolds and cone-manifolds
• Monodromy of hypergeometric functions and non-lattice integral monodromy
• Braid groups and Hodge theory
• The Burau representation is not faithful for \(n=5\)
• On Burau's representations at roots of unity
• A kernel of a braid group representation yields a knot with trivial knot polynomials
• The Burau representation is not faithful for \(n\geq 6\)
• Über Zopfgruppen und gleichsinnig verdrillte Verkettungen.
• The Faithfulness Question for the Burau Representation
• The Burau Representation is Unitary
• A note on the normal subgroups of mapping class groups
• Flat Surfaces
• DOES THE JONES POLYNOMIAL DETECT THE UNKNOT?
• Observed Periodicity Related to the Four-Strand Burau Representation
• Braid groups are linear
• Braid groups are linear

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