Topological recursion for the Poincar¨¦ polynomial of the combinatorial moduli space of curves

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• 作者：Motohico Mulase^a ; ^{mulase@math.ucdavis.edu} ; Michael Penkava^b ; ^{penkavmr@uwec.edu}
• 关键词：primary ; 14H15 ; 14N35 ; 05C30 ; 11P21 ; secondary ; 81T30
• 刊名：Advances in Mathematics
• 出版年：2012
• 出版时间：20 June, 2012
• 年：2012
• 卷：230
• 期：3
• 页码：1322-1339
• 全文大小：233 K

文摘

We show that the Poincar¨¦ polynomial associated with the orbifold cell decomposition of the moduli space of smooth algebraic curves with distinct marked points satisfies a topological recursion formula of the Eynard-Orantin type. The recursion uniquely determines the Poincar¨¦ polynomials from the initial data. Our key discovery is that the Poincar¨¦ polynomial is the Laplace transform of the number of Grothendieck¡¯s dessins d¡¯enfants.