The homological content of the Jones representations at $q = -1$

Jens Kristian Egsgaard; Søren Fuglede Jørgensen

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arXiv · 1402.6059

The homological content of the Jones representations at $q = -1$

Jens Kristian Egsgaard·Søren Fuglede Jørgensen

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Abstract

We generalize a discovery of Kasahara and show that the Jones representations of braid groups, when evaluated at $q = -1$, are related to the action on homology of a branched double cover of the underlying punctured disk. As an application, we prove for a large family of pseudo-Anosov mapping classes a conjecture put forward by Andersen, Masbaum, and Ueno by extending their original argument for the sphere with four marked points to our more general case.

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BibTeX RIS

Jens Kristian Egsgaard, Søren Fuglede Jørgensen. 2014-02-25. The homological content of the Jones representations at $q = -1$. https://arxiv.org/abs/1402.6059

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