The intersection form in the cohomology of the moduli space of genus 0 $n$-pointed curves $H^*(\overline{M}_{0,n})$ and the explicit K\"unneth formula in quantum cohomology

Abstract

We prove a general formula for the intersection form of two arbitrary monomials in boundary divisors. Furthermore we present a tree basis of the cohomology of $\overline {M}_{0,n}$. With the help of the intersection form we determine the Gram matrix for this basis and give a formula for its inverse. This enables us to calculate the tensor product of the higher order multiplications arising in quantum cohomology and formal Frobenius manifolds. In the context of quantum cohomology this establishes the explicit K\"unneth formula.