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

Seidel, Paul

doi:10.2140/gt.2012.16.2343

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Lagrangian homology spheres in $(A_{m})$ Milnor fibres via $\mathbb{C}^{*}$–equivariant $A_{\infty}$–modules

Paul Seidel

Geometry & Topology 16 (2012) 2343–2389

DOI: 10.2140/gt.2012.16.2343

Abstract

We establish restrictions on Lagrangian embeddings of spheres, and more generally 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–Ueda–Uehara concerning the derived categories of coherent sheaves on the resolutions of $(A_{m})$ surface singularities.

Keywords

Lagrangian submanifold, Floer cohomology, equivariant module

Mathematical Subject Classification 2010

Primary: 53D12

Secondary: 53D40, 16E45, 18E30

References

Publication

Received: 5 February 2012

Revised: 12 June 2012

Accepted: 16 July 2012

Published: 31 January 2013

Proposed: Richard Thomas

Seconded: Yasha Eliashberg, Leonid Polterovich

Authors

Paul Seidel
Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Ave Cambridge, MA 02139 United States
http://math.mit.edu/~seidel

Volume 16, issue 4 (2012)