Exact Lagrangian fillings of Legendrian $(2,n)$ torus links

Yu Pan

Vol. 289 (2017), No. 2, 417–441

DOI: 10.2140/pjm.2017.289.417

Abstract

Ekholm, Honda, and Kálmán constructed $C_n$ exact Lagrangian fillings for a Legendrian $\left(2,n\right)$ torus knot or link with maximal Thurston–Bennequin number, where $C_n$ is the $n$-th Catalan number. We show that these exact Lagrangian fillings are pairwise nonisotopic through exact Lagrangian isotopy. To do that, we compute the augmentations induced by the exact Lagrangian fillings $L$ to ${\mathbb{Z}}_2\left[H_1\left(L\right)\right]$ and distinguish the resulting augmentations.

Keywords

Exact Lagrangian fillings, (2,n) torus links, augmentation, Legendrian knots

Mathematical Subject Classification 2010

Primary: 53D42, 57R17

Milestones

Received: 1 August 2016

Revised: 13 January 2017

Accepted: 2 February 2017

Published: 19 June 2017