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

Baptiste Chantraine (1) , Lenhard Ng (2) , Steven Sivek (3)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 Duke University [Durham]
3 Imperial College London

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.

Domaines: Géométrie symplectique [math.SG]; Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Baptiste Chantraine, Lenhard Ng, Steven Sivek. Representations, sheaves, and Legendrian $(2,m)$ torus links. Journal of the London Mathematical Society, 2019, 100 (1), pp.41-82. ⟨hal-01873736⟩