Lagrangian homology spheres in (A_m) Milnor fibres via C^*-equivariant A_infinity modules

TL;DR

This paper investigates restrictions on Lagrangian embeddings of rational homology spheres into (A_m) Milnor fibres, using equivariant A-infinity modules and derived category techniques related to surface singularities.

Contribution

It introduces new restrictions on Lagrangian embeddings in Milnor fibres by applying equivariant A-infinity modules and derived category methods.

Findings

Restrictions on Lagrangian embeddings of rational homology spheres.

Application of equivariant objects in module categories.

Connections to derived categories of surface singularities.

Abstract

We establish restrictions on Lagrangian embeddings of rational homology spheres into certain open symplectic manifolds, namely the (A_m) Milnor fibres of odd complex dimension. This relies on general considerations about equivariant objects in module categories (which may be applicable in other situations as well), as well as results of Ishii-Uehara and Ishii-Ueda-Uehara concerning the derived categories of coherent sheaves on the resolutions of (A_m) surface singularities.