Timeline for What is the kernel of $i^*:H^*(\overline{\mathcal{M}}_{g,n},\mathbb{Q}) \to H^*(\overline{\mathcal{M}}_{g-1,n+2},\mathbb{Q})$?
Current License: CC BY-SA 4.0
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| Jul 24, 2019 at 9:31 | history | edited | issoroloap | CC BY-SA 4.0 |
added 9 characters in body
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| Jan 29, 2018 at 9:14 | comment | added | issoroloap | @DanPetersen, yes, I have the same feeling. For instance, imagine you want to define a sort of "compact type COhFT" replacing the loop axiom with the fact that the classes vanish on $\delta_{irr}$. Then the natural modification of the Givental group simply sums over stable trees instead of any stable graph. This action commutes with multiplying by "\lambda_g", so you can't get out of that ideal. This is how I got to asking this question. | |
| Jan 29, 2018 at 9:14 | comment | added | issoroloap | @JasonStarr, oops did I write it in reverse? I guess Dan edited it. Thanks Dan. | |
| Jan 29, 2018 at 6:16 | history | edited | Dan Petersen | CC BY-SA 3.0 |
edited body; edited title
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| Jan 29, 2018 at 6:14 | comment | added | Dan Petersen | At one point Hain and Looijenga conjectured that the ideal inside $R^\bullet(\overline M_{g,n})$ consisting of classes restricting trivially to the Deligne-Mumford boundary is principal, generated by $\lambda_g\lambda_{g-1}$. But it's not clear to me if this conjecture should be believed, this was part of a proposed generalization of the Faber conjecture. The analogue of this conjecture for "compact type" would be that the ideal of tautological classes restricting trivially to $\delta_{irr}$ is generated by $\lambda_g$; again, it's not clear if this should be believed. | |
| Jan 29, 2018 at 3:25 | comment | added | Jason Starr | Since cohomology is contravariant, did you intend to write $i^*$ in the opposite direction in your title and on Line 5? Also, since the "Satake contraction" of $\overline{\mathcal{M}}_{g,n}$ has positive-dimensional fibers on the image of $i$, you can produce elements in the kernel of the (contravariant) map $i^*$ by pulling back classes of cohomological degree $2(3g-4)$ by the Satake compactification, e.g., an appropriate power of $\lambda_1$. Is there reason to believe those classes are in the ideal generated by $\lambda_g$? | |
| Jan 29, 2018 at 0:36 | history | edited | issoroloap |
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| Jan 29, 2018 at 0:26 | history | asked | issoroloap | CC BY-SA 3.0 |