Lagrangian homology spheres in (Am) Milnor fibres via ℂ∗–equivariant A∞–modules

Seidel, Paul¹

¹ Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, MA 02139, United States

Geometry & topology, Tome 16 (2012) no. 4, pp. 2343-2389.

Résumé

We establish restrictions on Lagrangian embeddings of spheres, and more generally rational homology spheres, into certain open symplectic manifolds, namely the $\left(A_m\right)$ 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–Ueda–Uehara concerning the derived categories of coherent sheaves on the resolutions of $\left(A_m\right)$ surface singularities.

Détail

DOI : 10.2140/gt.2012.16.2343

Classification : 53D12, 53D40, 16E45, 18E30
Keywords: Lagrangian submanifold, Floer cohomology, equivariant module

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