### Book chapter

## Primary invariants of Hurwitz Frobenius manifolds

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?