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Topological recursion relations from Pixton relations

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Abstract

We propose an algorithm to derive tautological relations from Pixton relations. We carry out this algorithm explicitly to derive some results in genus 0, 1, 2, 3 and analyze the possibility to generalize to higher genera. As an application, some results about reconstruction of Gromov–Witten invariants can be derived.

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Acknowledgements

The first author would like to thank Xiaobo Liu for helpful discussions, and Yongbin Ruan for his interest in our work. We thank the referees for their useful comments and suggestions.

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Authors and Affiliations

  1. Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, P. R. China

    Yi Jie Lin & Jian Zhou

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  1. Yi Jie Lin
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  2. Jian Zhou
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Correspondence to Yi Jie Lin.

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The second author is partially supported by NSFC (Grant No. 11171174)

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Lin, Y.J., Zhou, J. Topological recursion relations from Pixton relations. Acta. Math. Sin.-English Ser. 33, 470–494 (2017). https://doi.org/10.1007/s10114-016-6155-2

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  • DOI: https://doi.org/10.1007/s10114-016-6155-2

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