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Categorification of the virtual braid groups

Anne-Laure Thiel (2011)

Annales mathématiques Blaise Pascal

We extend Rouquier’s categorification of the braid groups by complexes of Soergel bimodules to the virtual braid groups.

Cogrowth and spectral gap of generic groups

Yann Ollivier (2005)

Annales de l’institut Fourier

The cogrowth exponent of a group controls the random walk spectrum. We prove that for a generic group (in the density model) this exponent is arbitrarily close to that of a free group. Moreover, this exponent is stable under random quotients of torsion-free hyperbolic groups.

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