Recursion Between Mumford Volumes of Moduli Spaces
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- Eynard, B. Ann. Henri Poincaré (2011) 12: 1431. doi:10.1007/s00023-011-0113-4
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We propose a new proof, as well as a generalization of Mirzakhani’s recursion for volumes of moduli spaces. We interpret those recursion relations in terms of expectation values in Kontsevich’s integral, i.e., we relate them to a ribbon graph decomposition of Riemann surfaces. We find a generalization of Mirzakhani’s recursions to measures containing all higher Mumford’s κ classes, and not only κ1 as in the Weil–Petersson case.