Timeline for Exterior derivative on loop space
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Nov 5, 2019 at 7:09 | comment | added | Andrew Stacey | There's a chapter in Kreigel and Michor's book: the convenient setting of global analysis, where they discuss all the different ways of defining forms. I recommend reading it. | |
| May 19, 2019 at 17:03 | comment | added | domenico fiorenza | As Tobias remarks, the real question here is "How do vector fields on $LX$ (according to the given definition) act as derivations on smooth functions on $LX$?" And this is again as in the finite dimensional setting: consider a curve in $LX$ starting at $\gamma$ and with tangent vector at $t=0$ given by $v_\gamma$... | |
| May 19, 2019 at 7:56 | history | edited | Mattia Coloma | CC BY-SA 4.0 |
added 26 characters in body
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| May 19, 2019 at 7:55 | comment | added | Mattia Coloma | yes, of course. Thank you. | |
| May 19, 2019 at 3:26 | comment | added | cgodfrey | Minor detail but do you mean $\Omega^k(LX): = \Gamma(LX, \bigwedge^k TLX^\vee)$ (that is, $k$th exterior power of the cotangent bundle) | |
| May 18, 2019 at 19:21 | comment | added | Tobias Diez | The loop space is an infinite-dimensional manifold. Hence, the exterior differential is defined by the same formula as in the finite-dimensional setting. See for example these notes: math.uni-hamburg.de/home/wockel/data/monastir.pdf | |
| May 18, 2019 at 15:41 | history | asked | Mattia Coloma | CC BY-SA 4.0 |