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Invertible cohomological field theories and Weil-Petersson volumes

Yuri I. Manin, Peter Zograf (2000)

Annales de l'institut Fourier

We show that the generating function for the higher Weil–Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten’s free energy by a change of variables given by Schur polynomials. Since this generating function has a natural extension to the moduli space of invertible Cohomological Field Theories, this suggests the existence of a “very large phase space”, correlation functions on which include Hodge integrals studied by C. Faber and R. Pandharipande....

Singularities and normal forms of generic 2-distributions on 3-manifolds

B. Jakubczyk, M. Zhitomirskiĭ (1995)

Studia Mathematica

We give a complete classification of germs of generic 2-distributions on 3-manifolds. By a 2-distribution we mean either a module generated by two vector fields (at singular points its dimension decreases) or a Pfaff equation, i.e. a module generated by a differential 1-form (at singular points the dimension of its kernel increases).

The homotopy type of the space of degree 0 immersed plane curves.

Hiroki Kodama, Peter W. Michor (2006)

Revista Matemática Complutense

The space Bi0 = Imm0 (S1, R2) / Diff (S1) of all immersions of rotation degree 0 in the plane modulo reparameterizations has homotopy groups π1(Bi0) = Z, π2(Bi0) = Z, and πk(Bi0) = 0 for k ≥ 3.

Théorie de jauge et symétries des fibrés

D. Brandt, Jean-Claude Hausmann (1993)

Annales de l'institut Fourier

Soit ξ un G -fibré principal différentiable sur une variété M ( G un groupe de Lie compact). Étant donné une action d’un groupe de Lie compact Γ sur M , on se pose la question de savoir si elle provient d’une action sur le fibré ξ . L’originalité de ce travail est de relier ce problème à l’existence de points fixes pour les actions de Γ que l’on induit naturellement sur divers espaces de modules de G -connexions sur ξ .

Witten's Conjecture for many four-manifolds of simple type

Paul M. N. Feehan, Thomas G. Leness (2015)

Journal of the European Mathematical Society

We prove that Witten’s Conjecture [40] on the relationship between the Donaldson and Seiberg-Witten series for a four-manifold of Seiberg-Witten simple type with b 1 = 0 and odd b 2 + 3 follows from our ( 3 ) -monopole cobordism formula [6] when the four-manifold has c 1 2 χ h - 3 or is abundant.

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