Timeline for "Softness" vs "rigidity" in Geometry
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
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| Dec 12, 2012 at 19:04 | comment | added | Misha | A good example of "Lashof's demarcation" would be: De Rham theory (1st order derivatives) is topology, while Hodge theory (harmonicity) is geometry. However, parts of gauge theory (e.g. Donaldson, Floer, Seiberg-Witten) would be regarded as "geometry", even though they are traditionally treated as "topology". I guess, in this case, one could say that geometrically defined invariants are used to construct topological invariants, similarly to the situation with Hodge - de Rham theories. | |
| Dec 12, 2012 at 5:02 | comment | added | Misha | I think he meant that curvature is a 2nd order differential operator and that geodesics are solutions of 2nd order ODE. On the other hand, where would he place Morse functions, which are primarily (in finite dimensional setting) an object of differential topology, but are defined by a 2nd order condition. | |
| Dec 12, 2012 at 4:40 | comment | added | Will Sawin | can you expand on this? No idea what it means. | |
| Dec 12, 2012 at 4:09 | history | answered | Steven Landsburg | CC BY-SA 3.0 |