Datensatz

Zusammenfassung

A conjectural formula for the $k$-point generating function of Gromov-Witten
invariants of the Riemann sphere for all genera and all degrees was proposed in [11]. In this paper, we give a proof of this formula together with an explicit analytic (as opposed to formal) expression for the corresponding matrix resolvent. We also give a formula for the $k$-point function as a sum of $(k-1)!$ products of hypergeometric functions of one variable. We show that the $k$-point generating function coincides with the $\epsilon\rightarrow 0$
asymptotics of the analytic $k$-point function, and also compute three more asymptotics of the analytic function for $\epsilon\rightarrow \infty$, thus defining new invariants for the Riemann sphere.