Timeline for Analytic refinement of generalized cohomology theories
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 2, 2016 at 17:55 | comment | added | Andrei Halanay | @DmitriPavlov If you would expand your comment to an answer I'll able to vote and accept it. | |
| Nov 1, 2016 at 22:58 | comment | added | Dmitri Pavlov | Yes. Essentially it suffices to observe that complex manifolds look like a polydisk locally, so homotopy-invariant sheaves are once again equivalent to spaces. The rest of the construction proceeds in the same way. For example, using holomorphic differential forms instead of smooth forms one recovers holomorphic Deligne cohomology. | |
| Nov 1, 2016 at 18:16 | comment | added | David Roberts♦ | This would be neatly captured by what Urs Schreiber calls cohesive higher topos theory. Indeed his Habilitation is called "Differential cohomology in a cohesive $\infty$-topos" ncatlab.org/schreiber/show/…, but perhaps a more specific pertinent reference is arxiv.org/abs/1311.3188, which, together with the material at ncatlab.org/nlab/show/complex+analytic+%E2%88%9E-groupoid, should allow a differential holomorphic cohomology theory. | |
| Nov 1, 2016 at 17:24 | history | asked | Andrei Halanay | CC BY-SA 3.0 |