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POLYNOMIAL RECURSION FORMULA FOR LINEAR HODGE INTEGRALS
"... Abstract. We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the cutandjoin equation for the Laplace transform of the Hurwitz numbers. We show that the recursion recovers the WittenKontsevich theorem when restricted to the top degree terms, and also the comb ..."
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Abstract. We establish a polynomial recursion formula for linear Hodge integrals. It is obtained as the cutandjoin equation for the Laplace transform of the Hurwitz numbers. We show that the recursion recovers the WittenKontsevich theorem when restricted to the top degree terms, and also the combinatorial factor of the λg formula as the lowest degree terms. Dedicated to Herbert Kurke on the occasion of his 70th birthday Contents
Topological recursion for the Poincare polynomial of the combinatorial moduli space of curves
, 2010
"... We show that the Poincare 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 EynardOrantin type. The recursion uniquely determines the Poincaré polynomials from the ..."
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Cited by 10 (4 self)
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We show that the Poincare 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 EynardOrantin type. The recursion uniquely determines the Poincaré polynomials from the initial data. Our key discovery is that the Poincare ́ polynomial is the Laplace transform of the number of Grothendieck’s dessins d’enfants.
Topological recursion for symplectic volumes of moduli spaces of curves. arXiv:1010.1747v1 [math.SG
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MIRZAKHARNI’S RECURSION FORMULA IS EQUIVALENT TO THE WITTENKONTSEVICH THEOREM
, 2009
"... In this paper, we give a proof of Mirzakhani’s recursion formula of WeilPetersson volumes of moduli spaces of curves using the WittenKontsevich theorem. We also describe properties of intersections numbers involving higher degree κ classes. ..."
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Cited by 5 (3 self)
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In this paper, we give a proof of Mirzakhani’s recursion formula of WeilPetersson volumes of moduli spaces of curves using the WittenKontsevich theorem. We also describe properties of intersections numbers involving higher degree κ classes.
QUANTUM CURVES FOR HITCHIN FIBRATIONS AND THE EYNARDORANTIN THEORY
, 2014
"... We generalize the topological recursion of Eynard–Orantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347–452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic ..."
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Cited by 4 (3 self)
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We generalize the topological recursion of Eynard–Orantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347–452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle T ∗C of an arbitrary smooth base curve C. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal deformation family of D modules over an arbitrary projective algebraic curve C of genus greater than 1, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the SL(2,C)character variety of the fundamental group π1(C). We show that the semiclassical limit through the WKB approximation of these deformed D
Descendant integrals and tautological rings of moduli spaces of curves
, 2010
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The Kontsevich constants for the volume of the moduli of curves and topological recursion
"... We give an EynardOrantin type topological recursion formula for the canonical Euclidean volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion comes from the edge removal operation on the space of ribbon graphs. As an application we obtain a new proof of the Kont ..."
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Cited by 3 (1 self)
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We give an EynardOrantin type topological recursion formula for the canonical Euclidean volume of the combinatorial moduli space of pointed smooth algebraic curves. The recursion comes from the edge removal operation on the space of ribbon graphs. As an application we obtain a new proof of the Kontsevich constants for the ratio of