Equivalence of the Open KdV and the Open Virasoro Equations for the Moduli Space of Riemann Surfaces with Boundary
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In a recent paper, Pandharipande, Solomon and Tessler initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. The authors conjectured KdV and Virasoro type equations that completely determine all intersection numbers. In this paper, we study these equations in detail. In particular, we prove that the KdV and the Virasoro type equations for the intersection numbers on the moduli space of Riemann surfaces with boundary are equivalent.
KeywordsRiemann surfaces with boundary moduli space KdV equations
Mathematics Subject ClassificationPrimary 35Q53 Secondary 14H10
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