609 research outputs found
Foliations and webs inducing Galois coverings
We introduce the notion of Galois holomorphic foliation on the complex
projective space as that of foliations whose Gauss map is a Galois covering
when restricted to an appropriate Zariski open subset. First, we establish
general criteria assuring that a rational map between projective manifolds of
the same dimension defines a Galois covering. Then, these criteria are used to
give a geometric characterization of Galois foliations in terms of their
inflection divisor and their singularities. We also characterize Galois
foliations on admitting continuous symmetries, obtaining a
complete classification of Galois homogeneous foliations
Local symplectic field theory
Generalizing local Gromov-Witten theory, in this paper we define a local
version of symplectic field theory. When the symplectic manifold with
cylindrical ends is four-dimensional and the underlying simple curve is regular
by automatic transversality, we establish a transversality result for all its
multiple covers and discuss the resulting algebraic structures
Contact structures, deformations and taut foliations
Using deformations of foliations to contact structures as well as rigidity
properties of Anosov foliations we provide infinite families of examples which
show that the space of taut foliations in a given homotopy class of plane
fields is in general not path connected. Similar methods also show that the
space of representations of the fundamental group of a hyperbolic surface to
the group of smooth diffeomorphisms of the circle with fixed Euler class is in
general not path connected. As an important step along the way we resolve the
question of which universally tight contact structures on Seifert fibered
spaces are deformations of taut or Reebless foliations when the genus of the
base is positive or the twisting number of the contact structure in the sense
of Giroux is non-negative.Comment: 37 pages, 2 figures; Improved exposition incorporating referee's
comments mainly in Sections 5 and 9. (To appear in Geom. Topol.
Subdivision Directional Fields
We present a novel linear subdivision scheme for face-based tangent
directional fields on triangle meshes. Our subdivision scheme is based on a
novel coordinate-free representation of directional fields as halfedge-based
scalar quantities, bridging the finite-element representation with discrete
exterior calculus. By commuting with differential operators, our subdivision is
structure-preserving: it reproduces curl-free fields precisely, and reproduces
divergence-free fields in the weak sense. Moreover, our subdivision scheme
directly extends to directional fields with several vectors per face by working
on the branched covering space. Finally, we demonstrate how our scheme can be
applied to directional-field design, advection, and robust earth mover's
distance computation, for efficient and robust computation
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