Refining Witten-Kontsevich
Abstract.
The moduli space of metric Möbius graphs, which are non-orientable ribbon graphs, has one component homeomorphic to the moduli space of Riemann surfaces and another component homeomorphic to the moduli space of Klein surfaces. I'll discuss a lattice point count on this moduli space, weighted by a polynomial in b known as the measure of non-orientability. This "refined" lattice point count satisfies a refined version of Norbury's recursion for the count of lattice points on the moduli space of curves. Consequently, we obtain a recursion for the volumes of these moduli spaces that reduces to the Witten-Kontsevich recursion when b=0.
