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D. Kotschick

  1. Three-manifolds and Kaehler groups.

    Пт, 11/19/2010 - 16:01 — SomNambul
    Authors: D. Kotschick
    Subjects: Geometric Topology
    Abstract

    We give a simple proof of a result originally due to Dimca and Suciu: a group
    that is both Kaehler and the fundamental group of a closed three-manifold is
    finite. We also prove that a group that is both the fundamental group of a
    closed three-manifold and of a non-Kaehler compact complex surface is infinite
    cyclic or the direct product of an infinite cyclic group and a group of order
    two.

  2. Contact pairs and locally conformally symplectic structures.

    Чт, 06/03/2010 - 15:01 — SomNambul
    Authors: D. Kotschick, G. Bande
    Subjects: Symplectic Geometry
    Abstract

    We discuss a correspondence between certain contact pairs on the one hand,
    and certain locally conformally symplectic forms on the other. In particular,
    we characterize these structures through suspensions of contactomorphisms. If
    the contact pair is endowed with a normal metric, then the corresponding lcs
    form is locally conformally Kaehler, and, in fact, Vaisman. This leads to
    classification results for normal metric contact pairs.

  3. The Gelfand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations.

    Втр, 10/20/2009 - 12:53 — SomNambul
    Authors: D. Kotschick, S. Morita
    Subjects: Symplectic Geometry
    Abstract

    In the early 1970's, Gelfand, Kalinin and Fuks found an exotic characteristic
    class of degree 7 in the Gelfand-Fuks cohomology of the Lie algebra of formal
    Hamiltonian vector fields on the plane. We prove that this cohomology class can
    be decomposed as a product of a certain leaf cohomology class of degree 5 and
    the transverse symplectic class. This is similar to the well known
    factorization of the Godbillon-Vey class for codimension n foliations.

  4. Fibrations and fundamental groups of Kaehler-Weyl manifolds.

    Ср, 08/19/2009 - 19:30 — SomNambul
    Authors: G. Kokarev, D. Kotschick
    Subjects: Differential Geometry
    Abstract

    We extend the Siu--Beauville theorem to a certain class of compact
    Kaehler--Weyl manifolds, proving that they fiber holomorphically over
    hyperbolic Riemannian surfaces whenever they satisfy the necessary topological
    hypotheses. As applications we obtain restrictions on the fundamental groups of
    such Kaehler--Weyl manifolds, and show that in certain cases they are in fact
    Kaehler.

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