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arXiv · 1805.03603

Representations, sheaves, and Legendrian $(2,m)$ torus links

Baptiste Chantraine·Lenhard Ng·Steven Sivek
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Abstract

We study an $A_\infty$ category associated to Legendrian links in $\mathbb{R}^3$ whose objects are $n$-dimensional representations of the Chekanov-Eliashberg differential graded algebra of the link. This representation category generalizes the positive augmentation category and we conjecture that it is equivalent to a category of sheaves of microlocal rank $n$ constructed by Shende, Treumann, and Zaslow. We establish the cohomological version of this conjecture for a family of Legendrian $(2,m)$ torus links.

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Baptiste Chantraine, Lenhard Ng, Steven Sivek. 2018-05-09. Representations, sheaves, and Legendrian $(2,m)$ torus links. https://doi.org/10.1112/jlms.12204

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