Book Chapter

Primary invariants of Hurwitz Frobenius manifolds

P Dunin-Barkowski, P Norbury, N Orantin, A Popolitov, S Shadrin

Proceedings of Symposia in Pure Mathematics | AMER MATHEMATICAL SOC | Published : 2018

Abstract

Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds and the topological recursion formalism. We then apply this correspondence to Hurwitz Frobenius manifolds by explaining that the corresponding primary invariants can be obtained as periods of multidifferentials globally defined on a compact Riemann surface by topological recursion. Finally, we use this construction to reply to the following question in a large class of cases: given a compact Riemann surface, what does the topological recursion c..

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Funding Acknowledgements

The first author was partially supported by RFBR grants 16-31-60044-mol-a-dk and 15-01-05990, and by joint RFBR-India grant 16-51-45029-Ind.The fourth author was partially supported by RFBR grant 16-01-00291.The first and fourth authors were also partially supported by RFBR grant 15-31-20832-mol-a-ved and by joint RFBR-Japan grant 15-52-50041-YaF.The third and fourth authors were supported by the Netherlands Organisation for Scientific Research.