Timeline for Is there any geometrical/homological intuition behind symmetrized gradient?
Current License: CC BY-SA 4.0
7 events
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| Feb 27, 2019 at 20:31 | comment | added | Piotr Hajlasz | @Romeo I realized I do not have much to say and probably you know all what I know. I just wanted to list some work on spaces of bounded deformation, but I guess you know the literature. | |
| Feb 27, 2019 at 18:23 | comment | added | Romeo | @PiotrHajlasz I am sorry to bother you but, if you have some time, I would read with pleasure your comment/answer (especially concerning the link between BD functions and currents). Thanks a lot for your help. | |
| Jan 31, 2019 at 2:40 | comment | added | j.c. | This operator shows up in linear elasticity, see e.g. calvino.polito.it/~salamon/seminar/srni99.pdf ams.org/journals/bull/2010-47-02/S0273-0979-10-01278-4 and link.springer.com/article/10.1007/s00205-014-0806-1 for some work on the "elasticity complex". | |
| Jan 30, 2019 at 19:30 | comment | added | Paul Siegel | I'll also add that $d$ and symmetrized $d$ induce the same class in the K-homology of the underlying manifold, so one can pass freely back and forth between them for the purposes of index theory and such. | |
| Jan 30, 2019 at 19:28 | comment | added | Paul Siegel | Note that the gradient operator corresponds to the $d$ operator under the musical isomorphism, so for cohomological purposes it suffices to consider symmetrized $d$. If I'm not confusing myself, $d$ has the same kernel and cokernel as symmetrized $d$, both viewed as graded operators on the graded exterior algebra of the tangent bundle, so they are cohomologically equivalent (though doing computations with explicit representatives of cohomology classes may feel a bit different). | |
| Jan 30, 2019 at 18:58 | comment | added | Piotr Hajlasz | I know something about that and I will write what I know when I have time. If you do not see my answer within 24 hours, please leave a comment for me with a reminder since I may forget about your question. | |
| Jan 30, 2019 at 18:48 | history | asked | Romeo | CC BY-SA 4.0 |