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

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Journal Article

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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Duke Authors

Cited Authors

  • Chantraine, B; Ng, L; Sivek, S

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Published By

International Standard Serial Number (ISSN)

  • 0024-6107

Digital Object Identifier (DOI)

  • 10.1112/jlms.12204