Timeline for What is torsion in differential geometry intuitively?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2020 at 14:17 | comment | added | LSpice | I am amused that a later question tried to clear up the "notoriously slippery concept" of torsion by asking about the Rolling without slipping interpretation of torsion. | |
| S Mar 26, 2018 at 17:52 | history | suggested | CommunityBot | CC BY-SA 3.0 |
changed 'integrality' to 'integrability' (probably what was meant)
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| Mar 26, 2018 at 17:13 | review | Suggested edits | |||
| S Mar 26, 2018 at 17:52 | |||||
| May 20, 2017 at 20:06 | comment | added | R. van Dobben de Bruyn | More generally, it seems to me that the sheaf of torsion free connections should be a (sheaf) torsor under $\rho_1P$. The intrinsic torsion vanishes if and only if this torsor is trivial, i.e. the sheaf has a global section. | |
| Dec 16, 2012 at 1:36 | comment | added | David Corwin | Don't you mean GL_n(C) in GL_{2n}(R)? | |
| Dec 16, 2012 at 0:27 | history | edited | John Pardon | CC BY-SA 3.0 |
fixed spelling of "their"
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| Aug 2, 2010 at 11:58 | comment | added | Chris Schommer-Pries | @ algori: P is the G-principal bundle coming from the G-structure (see the link I provided) and $\rho_i(P)$ are the associated bundles induced by the representations $\rho_i$, which come from the short exact sequence I mention. Sorry if that was confusing. It seemed clear enough from context, but perhaps it wasn't. Anyway, I don't have my copy of Milnor and Stasheff handy, but I'm fairly certain this torsion is the same. Most of what I say is explained in more detail in D. Joyce's book "Compact Manifolds with Special Holonomy". I suggest looking there for more details. | |
| Aug 2, 2010 at 5:43 | comment | added | algori | Chris -- your answer is very interesting but a bit difficult to follow, in particular since you use some notation that you do not define ($P,\rho_1 P,\ldots$), so I'd like to ask: is this notion of torsion the same as in Sebastian's answer below (i.e. the same as the one given e.g. in Milnor-Stasheff, Characteristic classes, appendix C)? More precisely, we take a connection on the (co)tangent bundle compatible with a given $G$-structure on a manifold. In example 1 the answer is yes, so I was wondering about the other two. | |
| Apr 9, 2010 at 10:24 | vote | accept | Jan Weidner | ||
| Apr 7, 2010 at 7:29 | comment | added | Jan Weidner | This answer is just great, thank you very much! | |
| Apr 6, 2010 at 14:25 | history | answered | Chris Schommer-Pries | CC BY-SA 2.5 |