Anchored Lagrangian submanifolds and their Floer theory

Details Anchored Lagrangian submanifolds and their Floer theory Anchored Lagrangian submanifolds and their Floer theory

2009-07-13

arxiv.org/abs/0907.2122v1

Mathematics

Symplectic Geometry

40 pages

Scientific paper

We introduce the notion of (graded) anchored Lagrangian submanifolds and use it to study the filtration of Floer' s chain complex. We then obtain an anchored version of Lagrangian Floer homology and its (higher) product structures. They are somewhat different from the more standard non-anchored version. The anchored version discussed in this paper is more naturally related to the variational picture of Lagrangian Floer theory and so to the likes of spectral invariants. We also discuss rationality of Lagrangian submanifold and reduction of the coefficient ring of Lagrangian Floer cohomology of thereof.

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