Comparing tautological relations from the equivariant Gromov-Witten theory of projective spaces and spin structures

Abstract

Pandharipande-Pixton-Zvonkine's proof of Pixton's generalized Faber-Zagier relations in the tautological ring of ${\overline{M}}_{g,n}$ has started the study of tautological relations from semisimple cohomological field theories. In this article we compare the relations obtained in the examples of the equivariant Gromov-Witten theory of projective spaces and of spin structures. We prove an equivalence between the ${\mathbb{P}}^1$- and 3-spin relations, and more generally between restricted ${\mathbb{P}}^m$-relations and similarly restricted (m + 2)-spin relations. We also show that the general ${\mathbb{P}}^m$-relations imply the (m + 2)-spin relations.

Part of author's PhD thesis, result superseded by arXiv:1505.03419, 31 pages; v3: Appendix rewritten, various corrections

References in corpus (3)

• Relations in the tautological ring
• Conjectural relations in the tautological ring of ${\bar{M}}_{g,n}$
• Relations in the tautological ring of $M_g$

Cited by in corpus (6)

• Pixton's double ramification cycle relations
• The hypergeometric functions of the Faber-Zagier and Pixton relations
• Tautological relations via r-spin structures
• A Brief Survey of FJRW Theory
• The tautological ring of ${\mathcal{M}}_{g,n}$ via Pandharipande-Pixton-Zvonkine $r$-spin relations
• The moduli space of curves and its invariants