648 research outputs found

    Extended modular operad

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    This paper is a sequel to [LoMa] where moduli spaces of painted stable curves were introduced and studied. We define the extended modular operad of genus zero, algebras over this operad, and study the formal differential geometric structures related to these algebras: pencils of flat connections and Frobenius manifolds without metric. We focus here on the combinatorial aspects of the picture. Algebraic geometric aspects are treated in [Ma2].Comment: 38 pp., amstex file, no figures. This version contains additional references and minor change

    Morpho-logical Investigations: Wittgenstein and Spengler

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    The influence of Spengler on Wittgenstein's philosophical development is considered. The point of interest is in a significant methodological restructuring which it appears to have produced. After an initial over-enthusiastic reception, Wittgenstein is seen to object on some points which he attempted to emend in his own philosophy. Spengler's name disappeared inreworked manuscripts but traces persist in the Philosophical Investigations and an important section (§89-133) is found to be connected with it

    On Connection between Topological Landau-Ginzburg Gravity and Integrable Systems

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    We study flows on the space of topological Landau-Ginzburg theories coupled to topological gravity. We argue that flows corresponding to gravitational descendants change the target space from a complex plane to a punctured complex plane and lead to the motion of punctures.It is shown that the evolution of the topological theory due to these flows is given by dispersionless limit of KP hierarchy. We argue that the generating function of correlators in such theories are equal to the logarithm of the tau-function of Generalized Kontsevich Model.Comment: 17 p. late

    Anticommutativity Equation in Topological Quantum Mechanics

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    We consider topological quantum mechanics as an example of topological field theory and show that its special properties lead to numerous interesting relations for topological corellators in this theory. We prove that the generating function F\mathcal{F} for thus corellators satisfies the anticommutativity equation (DF)2=0(\mathcal{D}- \mathcal{F})^2=0. We show that the commutativity equation [dB,dB]=0[dB,dB]=0 could be considered as a special case of the anticommutativity equation.Comment: 6 pages, no figures, Late

    On the Length of the Relaxation Zone of Ionization Behind a Strong Shock Wave Front in the Air

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    Relaxation zone behind strong shock wave front in ai