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

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.

version 2: better results, simpler proofs; version 3: title changed as requested by referee, other very minor modifications

References in corpus (2)

• Symplectic cohomology and q-intersection numbers
• Fukaya categories of the torus and Dehn surgery

Cited by in corpus (8)

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• Disjoinable Lagrangian tori and semisimple symplectic cohomology
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• Symplectomorphisms and spherical objects in the conifold smoothing