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Abstract |
I will present a new formalism, which takes as input a functor $E$ from a category of surfaces with their mapping classes as morphisms, to a category of topological vector spaces, together with glueing operations, as well as a small amount of initial data, and produces as output functorial assignments $S \mapsto \Omega_S$ in $E(S)$. This construction is done by summing over all excisions of homotopy class of pair of pants decompositions of $S$, and we call it ``geometric recursion''. The topological recursion of Eynard and Orantin appears as a projection of the geometric recursion when $E(S)$ is chosen to be the space of continuous functions over the Teichmuller space of $S$, valued in a Frobenius algebra -- and the projection goes via integration over the moduli space. More generally, the geometric recursion aims at producing all kinds of mapping class group invariant quantities attached to surfaces. \\ \\ This is based on joint work with J.E. Andersen and N. Orantin. |
