Timeline for Explicit Spin Structures on the Torus
Current License: CC BY-SA 2.5
13 events
| when toggle format | what | by | license | comment | |
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| Mar 2, 2010 at 16:45 | answer | added | Tilman | timeline score: 3 | |
| Mar 2, 2010 at 9:58 | history | edited | Dmitri Pavlov |
edited tags
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| Jan 31, 2010 at 22:51 | answer | added | Tim Perutz | timeline score: 6 | |
| Jan 31, 2010 at 22:44 | answer | added | Dan Petersen | timeline score: 5 | |
| Jan 31, 2010 at 21:58 | answer | added | S. Carnahan♦ | timeline score: 3 | |
| Jan 31, 2010 at 21:33 | answer | added | Ryan Budney | timeline score: 6 | |
| Jan 31, 2010 at 21:13 | history | edited | john mangual | CC BY-SA 2.5 |
Added def'n of spin stricture. Corrected SU(2) to Spin(2)
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| Jan 31, 2010 at 20:52 | comment | added | john mangual | In the back of my head I was thinking the dimensions weren't right $Spin(2) = SO(2)$. Also, let me put in the specific definition of Spin structure from "Lectures on the Seiberg-Witten Invariants" by John Moore. | |
| Jan 31, 2010 at 17:26 | comment | added | Ryan Budney | Start with getting a feel for all the various equivalent defininitions of orientation here: mathoverflow.net/questions/10966/… then you'll have a launching pad for thinking about spin structures. For example, one way to say a tangent bundle admits a spin structure is it is orientable and every map $S^2 \to M$ admits a lift $S^2 \to O(TM)$. See item (2) in my post to the linked thread. Also see the references below, and the text by Milnor and Stasheff. | |
| Jan 31, 2010 at 8:47 | comment | added | Anirbit | Probably a very naive question in the context of this thread but still probably not fully out of context to request for detailed expositions on spin structures. Can you give references which will teach in details the whole idea of spin bundles and spin connections and spinors? | |
| Jan 30, 2010 at 21:26 | answer | added | José Figueroa-O'Farrill | timeline score: 5 | |
| Jan 30, 2010 at 21:20 | comment | added | Ryan Budney | There aren't any representations of $SU(2)$ on $T_pE$, as $SU(2)$ is a 3-dimensional compact Lie group, in particular it doesn't have any connected normal subgroups. Spin structures have many formulations, what flavour are you looking for? Usually you start by taking the direct sum of the tangent bundle with a trivial line bundle, when you're dealing with 2-dimensional vector bundles. | |
| Jan 30, 2010 at 21:10 | history | asked | john mangual | CC BY-SA 2.5 |