We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Floer homology on the universal cover, Audin's conjecture and other constraints on Lagrangian submanifolds.
- Authors
Damian, Mihai
- Abstract
We establish a new version of Floer homology for monotone Lagrangian embeddings in symplectic manifolds. As applications, we get assertions for monotone Lagrangian submanifolds L ↪ M which are displaceable through Hamiltonian isotopies (this happens for instance when M = Cn). We show that when L is aspherical, or more generally when the homology of its universal cover vanishes in odd degrees, its Maslov number NL equals 2. This is a generalization of Audin's conjecture. We also give topological characterisations of Lagrangians L ↪ M with maximal Maslov number: when NL = dim(L) + 1 then L is homeomorphic to a sphere; when NL = n ≥ 6 then L fibers over the circle and the fiber is homeomorphic to a sphere. A consequence is that any exact Lagrangian in T*S2kC1 whose Maslov class is zero is homeomorphic to S2kC1.
- Subjects
HOMOLOGY theory; LAGRANGIAN functions; MANIFOLDS (Mathematics); MASLOV index; MATHEMATICAL models
- Publication
Commentarii Mathematici Helvetici, 2012, Vol 87, Issue 2, p433
- ISSN
0010-2571
- Publication type
Article
- DOI
10.4171/CMH/259