No abstract

In this paper, we establish a relationship between the Weil- Petersson volume V g , n ( b ) V_{g,n}(b) of the moduli space M g , n ( b ) \mathcal {M}_{g,n}(b) of hyperbolic Riemann surfaces with geodesic boundary components of lengths b 1 b_{1} , …, b n b_{n} , and the intersection numbers of tautological classes on the moduli space M ¯ g , n \overline {\mathcal {M}}_{g,n} of stable curves. As a result, by using the recursive formula for V g , n ( b ) V_{g,n}(b) obtained in the author’s Simple geodesics and Weil-Petersson volumes of moduli spaces of bordered Riemann surfaces, preprint, 2003, we derive a new proof of the Virasoro constraints for a point. This result is equivalent to the Witten-Kontsevich formula.

Abstract. We prove results about orbit closures and equidistribution for the SL(2, R) action on the moduli space of compact Riemann surfaces, which are analogous to the theory of unipotent flows. The proofs of the main theorems rely on the measure classification theorem of [EMi2] and a certain isolation property of closed SL(2, R) invariant manifolds developed in this paper.

No abstract

No abstract