Translator Disclaimer
January 2022 Infinitely many Lagrangian fillings
Roger Casals, Honghao Gao
Author Affiliations +
Ann. of Math. (2) 195(1): 207-249 (January 2022). DOI: 10.4007/annals.2022.195.1.3

Abstract

We prove that all maximal-tb positive Legendrian torus links $(n,m)$ in the standard contact $3$-sphere, except for $(2,m)$, $(3,3)$, $(3,4)$ and $(3,5)$, admit infinitely many Lagrangian fillings in the standard symplectic 4-ball. This is proven by constructing infinite order Lagrangian concordances that induce faithful actions of the modular group $\mathrm{PSL}(2,\mathbb{Z})$ and the mapping class group $M_{0,4}$ into the coordinate rings of algebraic varieties associated to Legendrian links. In particular, our results imply that there exist Lagrangian concordance monoids with subgroups of exponential-growth, and yield Stein surfaces homotopic to a $2$-sphere with infinitely many distinct exact Lagrangian surfaces of higher-genus. We also show that there exist infinitely many satellite and hyperbolic knots with Legendrian representatives admitting infinitely many exact Lagrangian fillings.

Citation

Download Citation

Roger Casals. Honghao Gao. "Infinitely many Lagrangian fillings." Ann. of Math. (2) 195 (1) 207 - 249, January 2022. https://doi.org/10.4007/annals.2022.195.1.3

Information

Published: January 2022
First available in Project Euclid: 21 December 2021

Digital Object Identifier: 10.4007/annals.2022.195.1.3

Subjects:
Primary: 53D10
Secondary: 53D15 , 57R17

Keywords: cluster structures , Lagrangian fillings , Legendrian knots , microlocal sheaves , ping-pong Lemma

Rights: Copyright © 2022 Department of Mathematics, Princeton University

JOURNAL ARTICLE
43 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.195 • No. 1 • January 2022
Back to Top