Timeline for Simply put Floer homology
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 25, 2019 at 12:18 | comment | added | Marion | That is fair. It is one thing that you dont understand and another thing to not know that maybe my question cannot be understood or interpreted physically. | |
| Sep 23, 2019 at 13:46 | comment | added | mme | I meant no offense and intended no sarcasm. I mean very seriously when I say I wish I understood what "Floer homology" really was. The way I think about tends to be very formal and the pictures I have in my head are chosen to fit the analytic details as opposed to having some sort of general understanding. I am not sure if there is a physical interpretation or not (nor am I sure precisely what that would mean); I once asked a physicist but did not understand the response, which is more emblematic of my understanding of physics than anything else. | |
| Sep 23, 2019 at 10:56 | comment | added | Todd Trimble | Marion, to my eyes, there was no sarcasm or mockery. In fact, I see it as expressing sympathy and commiseration. | |
| Sep 23, 2019 at 9:42 | comment | added | Marion | @MikeMiller I have no way to know if Floer homology is a difficult topic for people working on the field or not, and I have no idea if there is a physical interpretation. Your comment, with the sarcasm it entails has no position in stack exchange. Mocking my question, even in a not mean way, is rude. As I stated I am a physicist thus I ask here for some information not a course. Look at Chris's comment, that is what I am looking for, comments in that direction. | |
| Sep 20, 2019 at 1:40 | comment | added | mme | "I would like to understand what exactly Floer homology of a 3-manifold is." So would I, and, I imagine, every other researcher in the area. There is certainly not some obvious space it is the singular cohomology of. In a few cases (not instanton!) there is a "spectrum" that Floer homology is the homology of. But the constructions are not so enlightening as you might like. | |
| Sep 19, 2019 at 23:10 | comment | added | Chris Gerig | Generators of Floer chain complex = objects defined over Y (such as connections, or embedded circles). Differential = certain count of objects on Y x R (R = reals) which are “asymptotic to” the generators on Y (as you move towards $\pm\infty$). What you should look up, that is similar in spirit, is Morse homology of a manifold. | |
| Sep 19, 2019 at 19:20 | comment | added | Neil Hoffman | One comment is that the three sphere is the only simply connected compact 3-manifold (without boundary). Would you want to restate the question in terms of simple integral homology spheres? | |
| Sep 19, 2019 at 19:16 | history | edited | Neil Hoffman | CC BY-SA 4.0 |
Minor formatting changes. Added 'is' to the first sentence.
|
| Sep 19, 2019 at 15:59 | history | asked | Marion | CC BY-SA 4.0 |