arXiv subjects

Yan-Lung Leon Li

Publications and source records attributed to Yan-Lung Leon Li.

3 recordsLinked to original sources

arXiv2026

Moment Lagrangians, unobstructedness and symplectic groupoids

Moment Lagrangian $L_μ$ is a Lagrangian in $T^*G^- \times Y^- \times Y$ associated to a Hamiltonian $G$-space $Y$ with a moment map $μ$. In this paper, we prove that $L_μ$ is tautologically unobstructed under mild assumptions on $Y$. As a key ingredient in the proof, we constructed a new symplectic groupoid structure on $T^*G^- \times Y^- \times Y$ over $G\times Y$ for which $L_μ$ is simultaneously the unit and the fixed locus of the inversion, which might be of independent interest.

math.SG↗

arXiv2026

Equivariant Partially Wrapped Fukaya Categories on Liouville Sectors

We develop an equivariant Lagrangian Floer theory for Liouville sectors that have symmetry of a Lie group $G$. Moreover, for Liouville manifolds with $G$-symmetry, we develop a correspondence theory to relate the equivariant Lagrangian Floer cohomology upstairs and Lagrangian Floer cohomology of its quotient. Furthermore, we study the symplectic quotient in the presence of nodal type singularities and prove that the equivariant correspondence gives an isomorphism on cohomologies which was conjectured by Lekili-Segal.

math.SG↗

arXiv2025

Equivariant Lagrangian correspondence and a conjecture of Teleman

In this paper, we study the Floer theory of equivariant Lagrangian correspondences and apply it to derive precise relations between the disc potential of an invariant Lagrangian submanifold and that of its quotient, thereby addressing a conjecture of Teleman. Furthermore, we proved that their (equivariant) Lagrangian Floer cohomologies are isomorphic. In particular, the functor by equivariant Lagrangian correspondence induces a quasi-isomorphism between the equivariant derived Fukaya category at a regular moment-map level and the derived Fukaya category of the corresponding symplectic quotient. A key step is to extend Fukaya's construction of an $A_\infty$ tri-module for Lagrangian correspondences to Borel spaces. We demonstrate that the equivariant obstruction of a Lagrangian correspondence plays an essential role, which leads to quantum corrections in the disc potentials of the quotients. We computed the disc potential of the Lagrangian correspondence in the toric setup and relate it with mirror maps for compact semi-Fano toric manifolds.

math.SG↗