Frobenius Manifolds near the Discriminant and Relations in the Tautological Ring

Abstract

We give a criterion for extending a generically semisimple (not necessarily conformal) Frobenius manifold locally near a smooth point of the discriminant to a cohomological field theory. As an application, we show that a large set of tautological relations related to the Givental--Teleman classification for any generically semisimple cohomological field theories follow from Pixton's generalized Faber--Zagier relations.

Part of author's PhD thesis, 28 pages, v3: Section 2 simplified using results of Hertling, agrees with published version, v2: Section 3 rewritten to include result on extending Frobenius manifolds to CohFTs

References in corpus (1)

• Relations on ${\overline{M}}_{g,n}$ via equivariant Gromov-Witten theory of ${\mathbb{P}}^1$

Cited by in corpus (5)

• Gromov-Witten theory of elliptic fibrations: Jacobi forms and holomorphic anomaly equations
• Combinatorics of Bousquet-Mélou-Schaeffer numbers in the light of topological recursion
• Relations on ${\overline{\mathcal{M}}}_{g,n}$ and the negative $r$-spin Witten conjecture
• Universal equations for higher genus Gromov-Witten invariants from Hodge integrals
• The tautological ring of ${\overline{\mathcal{M}}}_{g,n}$ is rarely Gorenstein