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Regular version of the site

Book chapter

Primary invariants of Hurwitz Frobenius manifolds

P. 297-331.
Dunin-Barkowski P., Norbury P., Orantin N., Popolitov A., Shadrin S.

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











In book

Primary invariants of Hurwitz Frobenius manifolds
Vol. 100: Topological Recursion and its Influence in Analysis, Geometry, and Topology. Providence: American Mathematical Society, 2018.