Orbifold GW theory as the Hurwitz-Frobenius submanifold (Q2636593)

The main result of this paper is beautifully summarized in its title: the Frobenius manifold of the orbifold GW-theory of \(\mathbb{P}^1(2,2,2,2)\) is a submanifold in a certain Hurwitz-Frobenius manifold. The GW theory of the orbifold \(\mathbb{P}^1(2,2,2,2)\) is reviewed in Section 2. The flat coordinates on the Hurwitz-Frobenius manifold \(\mathcal{H}_{1;(2,2,2,2)}\) is given in Section 3. The structure constants and their restriction to submanifolds are computed in Section 4 and Section 5, respectively. The main result is proved in Section 6.