@article{0b59deaa99d743a1b6481db9b23ef067,
title = "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{\textquoteright}s generalized Faber–Zagier relations.",
keywords = "Cohomological field theories, Discriminant, Frobenius manifolds, Tautological ring",
author = "Felix Janda",
note = "Funding Information: Acknowledgements The author is very grateful for various discussions with A. Buryak, E. Clader, Y.P. Lee, D. Petersen, R. Pandharipande, C. Schiessl, S. Shadrin and D. Zvonkine. The author has learned about the method of obtaining relations by studying a CohFT near the discriminant from D. Zvonkine at the conference Cohomology of the moduli space of curves organized by the Forschungs-institut f{\"u}r Mathematik at ETH Z{\"u}rich in 2013. D. Zvonkine there also expressed an idea why we should obtain the same relations from different CohFTs. Together with S. Shadrin he studied them in comparison with relations obtained from degree considerations (see Remark 3.20). The results on the extension of a Frobenius manifold to a CohFT is motivated from discussions with M. Kazarian, T. Milanov and D. Zvonkine at the workshop Geometric Invariants and Spectral Curves at the Lorentz Center in Leiden. Special thanks are due to an anonymous referee for drawing the author{\textquoteright}s attention to Hertling{\textquoteright}s work on Frobenius manifolds. This research was carried out while being a PhD. student of R. Pandharipande at ETH Z{\"u}rich and being supported by the Swiss National Science Foundation Grant SNF 200021_143274. Publisher Copyright: {\textcopyright} 2018, Springer Science+Business Media B.V., part of Springer Nature.",
year = "2018",
month = jul,
day = "1",
doi = "10.1007/s11005-018-1047-2",
language = "English (US)",
volume = "108",
pages = "1649--1675",
journal = "Letters in Mathematical Physics",
issn = "0377-9017",
publisher = "Springer",
number = "7",
}