Timeline for Monopole Floer Homology vs. Heegaard-Floer theory
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 25, 2017 at 5:34 | vote | accept | Nati | ||
| Apr 23, 2017 at 0:57 | comment | added | Nati | Also, Heegaard Floer theory comes from Lagrangian Floer homology so it has an $A_\infty$-structure, does the isomorphism identify it with something similar on the monopole side? | |
| Apr 21, 2017 at 22:19 | comment | added | mme | Heegaard Floer homology does not have an $A_\infty$-structure; it's the intersection homology of two different Lagrangians. (You might think you retain a module structure over the cohomology of the Lagrangians, but you lose this in handleslides.) The $A_\infty$-structure on the Fukaya category is useful in proving invariance eg under handleslides. As Chris Gerig says in his answer, the bordered theory does naturally associate an $A_\infty$-algebra to a surface and an $A_\infty$-module to a 3-manifold with boundary, but this is I think somewhat different than the question in your comment. | |
| Apr 21, 2017 at 21:58 | answer | added | Chris Gerig | timeline score: 6 | |
| Apr 21, 2017 at 17:19 | comment | added | Nati | @LiviuNicolaescu Thanks! I guess that answers the question of the relation between them ... is there some physical reason/intuition for it? | |
| Apr 21, 2017 at 16:59 | comment | added | Liviu Nicolaescu | arxiv.org/abs/1204.0115 | |
| Apr 21, 2017 at 16:03 | history | asked | Nati | CC BY-SA 3.0 |