Timeline for Why believe Kontsevich cosheaf conjecture?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2021 at 10:08 | history | edited | Jonny Evans | CC BY-SA 4.0 |
John Pardon pointed out an error which I'm flagging up
|
| Jan 1, 2021 at 10:01 | comment | added | Jonny Evans | Thanks for the clarifying comments, John! | |
| Dec 31, 2020 at 21:49 | comment | added | John Pardon | In fact, even in the case of an arboreal skeleton, the cosheaf depends on more than just the local topology of the skeleton. For example, at the simplest arboreal singularity (the A2 "tripod" singularity, i.e. a trivalent vertex) the category depends on the cyclic ordering of the three incident edges induced by the ambient symplectic structure. | |
| Dec 31, 2020 at 21:47 | comment | added | John Pardon | What the example of a ball union a single critical handle does show is that the Kontsevich--Nadler sheaf of categories depends on more than just the topology of the core (the costalk at the cone point will be the partially wrapped Fukaya category of the ball stopped at the attaching locus, whereas everywhere else the costalk will simply be Perf Z). | |
| Dec 31, 2020 at 21:46 | comment | added | John Pardon | The validity of the conjecture does not depend on having an arboreal skeleton. For example, the descent result here arxiv.org/abs/1809.03427 doesn't even make reference to the skeleton (or take the comparison with microlocal sheaves from arxiv.org/abs/1809.08807 and note that compact objects in microlocal sheaves form a cosheaf of categories). In the example of a ball with a single critical handle attached, there is a simple two-element sectorial cover to which the descent result applies. | |
| Dec 31, 2020 at 13:41 | history | edited | Jonny Evans | CC BY-SA 4.0 |
Added a clarification of assumptions you need to impose for the conjecture to hold
|
| Dec 30, 2020 at 19:17 | history | answered | Jonny Evans | CC BY-SA 4.0 |