The asymptotic Weil-Petersson form and intersection theory on M_{g,n}

Details The asymptotic Weil-Petersson form and intersection theory on M_{g,n} The asymptotic Weil-Petersson form and intersection theory on M_{g,n}

2010-10-20

arxiv.org/abs/1010.4126v1

Mathematics

Geometric Topology

22 pages

Scientific paper

Moduli spaces of hyperbolic surfaces with geodesic boundary components of fixed lengths may be endowed with a symplectic structure via the Weil-Petersson form. We show that, as the boundary lengths are sent to infinity, the Weil-Petersson form converges to a piecewise linear form first defined by Kontsevich. The proof rests on the observation that a hyperbolic surface with large boundary lengths resembles a graph after appropriately scaling the hyperbolic metric. We also include some applications to intersection theory on moduli spaces of curves.

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