Advances in Theoretical and Mathematical Physics

Volume 15 (2011)

Number 5

The n-point functions for intersection numbers on moduli spaces of curves

Pages: 1201 – 1236



Kefeng Liu (Zhejiang University, Hangzhou, China)

Hao Xu (University of California at Los Angeles)


Using the celebrated Witten--Kontsevich theorem, we provea recursive formula of the $n$-point functions forintersection numbers on moduli spaces of curves. It hasbeen used to prove the Faber intersection number conjectureand motivated us to find some conjectural vanishingidentities for Gromov--Witten invariants. The latter hasbeen proved recently by Liu and Pandharipande. We alsogive a combinatorial interpretation of $n$-point functionsin terms of summation over binary trees.

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