838 research outputs found

    Connected components of the moduli spaces of Abelian differentials with prescribed singularities

    Full text link
    Consider the moduli space of pairs (C,w) where C is a smooth compact complex curve of a given genus and w is a holomorphic 1-form on C with a given list of multiplicities of zeroes. We describe connected components of this space. This classification is important in the study of dynamics of interval exchange transformations and billiards in rational polygons, and in the study of geometry of translation surfaces.Comment: 42 pages, 12 figures, LaTe

    A remark on the matrix Airy function

    Full text link
    An integral representation for matrix Airy function is presentedComment: 4 page

    An algebra of deformation quantization for star-exponentials on complex symplectic manifolds

    Get PDF
    The cotangent bundle T∗XT^*X to a complex manifold XX is classically endowed with the sheaf of \cor-algebras \W[T^*X] of deformation quantization, where \cor\eqdot \W[\rmptt] is a subfield of \C[[\hbar,\opb{\hbar}]. Here, we construct a new sheaf of \cor-algebras \TW[T^*X] which contains \W[T^*X] as a subalgebra and an extra central parameter tt. We give the symbol calculus for this algebra and prove that quantized symplectic transformations operate on it. If PP is any section of order zero of \W[T^*X], we show that \exp(t\opb{\hbar} P) is well defined in \TW[T^*X].Comment: Latex file, 24 page

    Quantum Cohomology of a Product

    Full text link
    The operation of tensor product of Cohomological Field Theories (or algebras over genus zero moduli operad) introduced in an earlier paper by the authors is described in full detail, and the proof of a theorem on additive relations between strata classes is given. This operation is a version of the Kuenneth formula for quantum cohomology. In addition, rank one CohFT's are studied, and a generalization of Zograf's formula for Weil-Petersson volumes is suggested.Comment: AMSTex file, 30 pages. Figures (hard copies) available from Yu. Manin. Main paper by M. Kontsevich, Yu. Manin, appendix by R. Kaufman

    Poisson actions up to homotopy and their quantization

    Full text link
    Symmetries of Poisson manifolds are in general quantized just to symmetries up to homotopy of the quantized algebra of functions. It is therefore interesting to study symmetries up to homotopy of Poisson manifolds. We notice that they are equivalent to Poisson principal bundles and describe their quantization to symmetries up to homotopy of the quantized algebras of functions.Comment: 8 page

    On the variational noncommutative Poisson geometry

    Get PDF
    We outline the notions and concepts of the calculus of variational multivectors within the Poisson formalism over the spaces of infinite jets of mappings from commutative (non)graded smooth manifolds to the factors of noncommutative associative algebras over the equivalence under cyclic permutations of the letters in the associative words. We state the basic properties of the variational Schouten bracket and derive an interesting criterion for (non)commutative differential operators to be Hamiltonian (and thus determine the (non)commutative Poisson structures). We place the noncommutative jet-bundle construction at hand in the context of the quantum string theory.Comment: Proc. Int. workshop SQS'11 `Supersymmetry and Quantum Symmetries' (July 18-23, 2011; JINR Dubna, Russia), 4 page

    Lower bounds for Lyapunov exponents of flat bundles on curves

    No full text

    The Geometry of the Master Equation and Topological Quantum Field Theory

    Get PDF
    In Batalin-Vilkovisky formalism a classical mechanical system is specified by means of a solution to the {\sl classical master equation}. Geometrically such a solution can be considered as a QPQP-manifold, i.e. a super\m equipped with an odd vector field QQ obeying {Q,Q}=0\{Q,Q\}=0 and with QQ-invariant odd symplectic structure. We study geometry of QPQP-manifolds. In particular, we describe some construction of QPQP-manifolds and prove a classification theorem (under certain conditions). We apply these geometric constructions to obtain in natural way the action functionals of two-dimensional topological sigma-models and to show that the Chern-Simons theory in BV-formalism arises as a sigma-model with target space ΠG\Pi {\cal G}. (Here G{\cal G} stands for a Lie algebra and Π\Pi denotes parity inversion.)Comment: 29 pages, Plain TeX, minor modifications in English are made by Jim Stasheff, some misprints are corrected, acknowledgements and references adde