Invertible Cohomological Field Theories and Weil-Petersson volumes

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dc.creatorManin, Yu. I.
dc.creatorZograf, P.
dc.date1999-02-08
dc.date1999-04-12
dc.date.accessioned2026-07-07T05:27:50Z
dc.date.available2026-07-07T05:27:50Z
dc.descriptionWe show that the generating function for the higher Weil-Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten's free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a ``very large phase space'', correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande. From this formula we derive an asymptotical expression for the Weil-Petersson volume as conjectured by C. Itzykson. We also discuss a topological interpretation of the genus expansion formula of Itzykson-Zuber, as well as a related bialgebra acting upon quantum cohomology as a complex version of the classical path groupoid.
dc.description16 pages, AMSTex. The article is considerably enlarged. The derivation of asymptotical formulas for Weil-Petersson volumes is added and the topological meaning of some Itzykson-Zuber formulas is discussed. Several misprints are corrected
dc.identifierhttps://arxiv.org/abs/math/9902051
dc.identifierhttp://arxiv.org/abs/math/9902051
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/78074
dc.subjectAlgebraic Geometry
dc.titleInvertible Cohomological Field Theories and Weil-Petersson volumes
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