Timeline for Generator of a Fukaya category with certain properties
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 17, 2010 at 16:46 | comment | added | Tim Perutz | I haven't thought of one, but the conditions look more realistic now. | |
| Sep 17, 2010 at 15:29 | comment | added | Daniel Pomerleano | Ok I see what you are both saying about the product... But even if I lower my restrictions and ask for a Z/2Z graded Fukaya category which is generated by an orthogonal set of Lagrangians which are not spheres or products and keep the idea that HF(L,L) should be "defined over C" and admit vector space iso with cohomology, it sounds like even still we don't know such an example? | |
| Sep 17, 2010 at 14:59 | comment | added | Tim Perutz | Mohammed is quite right (and I missed) that if $m_2$ is classical, that may well be for a geometric reason that also makes higher structure classical; e.g. look at the diagonal in $X_-\times X$, whose HF is $QH^\ast(X)$. The product is undeformed if $X$ is symplectically aspherical, say, but then there can be no non-classical higher structure either. And I don't know an example of a monotone Lagrangian torus whose primary deformation class (a quadratic form) is trivial but whose secondary class is not. | |
| Sep 17, 2010 at 3:44 | comment | added | Daniel Pomerleano | Thanks Tim for taking me through the issues. This is kind of what I thought the theoretical status was... but it's great to hear an expert opinion. | |
| Sep 16, 2010 at 19:09 | history | answered | Tim Perutz | CC BY-SA 2.5 |