Abstract
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.
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Communicated by Marcos Marino.
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Eynard, B. Recursion Between Mumford Volumes of Moduli Spaces. Ann. Henri Poincaré 12, 1431–1447 (2011). https://doi.org/10.1007/s00023-011-0113-4
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DOI: https://doi.org/10.1007/s00023-011-0113-4