Let M be an n-dimensional Frobenius manifold. Fix \(\kappa \in \{1,\dots ,n\}\) . Assuming certain invertibility, Dubrovin introduced the Legendre-type transformation \(S_\kappa \) , which transforms M to an n-dimensional Frobenius manifold \(S_\kappa (M)\) . In this paper, we show that these \(S_\kappa (M)\) share the same monodromy data at the Fuchsian singular point of the Dubrovin connection, and that for the case when M is semisimple they also share the same Stokes matrix and the same central connection matrix. A straightforward application of the monodromy identification is the following: if we know the monodromy data of some semisimple Frobenius manifold M, we immediately obtain those of its Legendre-type transformations. Another application gives the identification between the \(\kappa \) th partition function of a semisimple Frobenius manifold M and the topological partition function of \(S_{\kappa }(M)\) .
