D. Kotschick
Three-manifolds and Kaehler groups.
Fri, 11/19/2010 - 16:01 — SomNambulAuthors: D. Kotschick
Subjects: Geometric Topology
AbstractWe 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.Contact pairs and locally conformally symplectic structures.
Thu, 06/03/2010 - 15:01 — SomNambulAuthors: D. Kotschick, G. Bande
Subjects: Symplectic Geometry
AbstractWe 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.The Gelfand-Kalinin-Fuks class and characteristic classes of transversely symplectic foliations.
Tue, 10/20/2009 - 12:53 — SomNambulAuthors: D. Kotschick, S. Morita
Subjects: Symplectic Geometry
AbstractIn 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.Fibrations and fundamental groups of Kaehler-Weyl manifolds.
Wed, 08/19/2009 - 19:30 — SomNambulAuthors: G. Kokarev, D. Kotschick
Subjects: Differential Geometry
AbstractWe 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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