@article{307ecf54508e4b1ba1d4b0bf240c1f2c,

title = "Topological Recursion Relations from Pixton{\textquoteright}s Formula",

abstract = "We prove that every degree-g polynomial in the ψ-classes on Mg,n can be expressed as a sum of tautological classes supported on the boundary with no κ-classes. Such equations, which we refer to as topological recursion relations, can be used to deduce universal equations for the Gromov–Witten invariants of any target.",

author = "Emily Clader and Felix Janda and Xin Wang and Dmitry Zakharov",

note = "Funding Information: Proof of Theorem 1. First, we use induction on n. The base case is when n = 1, in which case the result holds by Theorem 9. Suppose, then, that the result holds on Mg,n−1, and consider a degree-g ψ-monomial on Mg,n. If some ψj does not appear in this monomial, then modulo boundary, it is pulled back from Mg,n−1, and thus a TRR exists by induction. Thus, it suffices to consider ψ-monomials of the form (9) in which lj ≥ 1 for each j . For these monomials, induction on the lj together with Proposition 13 completes the proof. □ ACKNOWLEDGMENTS. The authors would like to thank Samuel Grushevsky, Xi-aobo Liu, Aaron Pixton, and Dustin Ross for useful discussions and inspiration. We specially thank an anonymous referee for their careful reading and very valuable advice for improving our results. The first author was partially supported by NSF DMS grant 1810969, the second author was partially supported by the CNRS and NSF DMS grant 2054830, and the third author was partially supported by NSFC grant 12071255 and SPNSF grant ZR2021MA101. Publisher Copyright: {\textcopyright} 2023 University of Michigan. All rights reserved.",

year = "2023",

month = may,

doi = "10.1307/mmj/20195795",

language = "English",

volume = "73",

pages = "227--241",

journal = "Michigan Mathematical Journal",

issn = "0026-2285",

publisher = "Michigan Mathematical Journal",

number = "2",

}