Transversely affine and transversely projective holomorphic foliations
نویسندگان
چکیده
منابع مشابه
Transversely Projective Structures on a Transversely Holomorphic Foliation
The space of transversely projective structures on a transversely holomorphic foliation is described. Some applications are given.
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The results of Biswas (2000) are extended to the situation of transversely projective foliations. In particular, it is shown that a transversely holomorphic foliation defined using everywhere locally nondegenerate maps to a projective space CPn, and whose transition functions are given by automorphisms of the projective space, has a canonical transversely projective structure. Such a foliation ...
متن کاملTransversely Projective Structures on a Transversely Holomorphic Foliation, Ii
Given a transversely projective foliation F on a C∞ manifold M and a nonnegative integer k, a transversal differential operator DF (2k + 1) of order 2k + 1 from N⊗k to N⊗(−k−1) is constructed, where N denotes the normal bundle for the foliation. There is a natural homomorphism from the space of all infinitesimal deformations of the transversely projective foliation F to the first cohomology of ...
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We establish a geometric condition that determines when a type III von Neumann algebra arises from a foliation whose holonomy becomes affine with respect to a suitable transverse coordinate system. Under such an assumption the Godbillon-Vey class of the foliation becomes trivial in contrast to the case considered in Connes’s famous theorem.
متن کاملFatou and Julia Components of Transversely Holomorphic Foliations
In this paper we study foliations F on compact manifolds M , of real codimension 2, with a transversal holomorphic structure. We construct a decomposition of M into dynamically defined components, similar to the Fatou/Julia sets for iteration of rational functions, or the region of discontinuity/limit set partition for Kleinian groups in PSL(2,C). All this in tune with Sullivan’s well known dic...
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ژورنال
عنوان ژورنال: Annales Scientifiques de l’École Normale Supérieure
سال: 1997
ISSN: 0012-9593
DOI: 10.1016/s0012-9593(97)89918-1