We show that there are algorithms to determine if a 3-manifold contains an essential lamination or a Reebless foliation. AMS Classification numbers Primary: 57M50

This foliation is nonorientable and it has a transversal measure. The measure can be given locally out of the singularities by a closed 1-form. Half translation surfaces. Let M be a two-dimensional surface with a flat metric which has only conical singularities. The surface is called a half translation if the holonomy along any path on the surface is either Id or -Id. It is clear that the angle...

This work concerns the problem of relating characteristic numbers of onedimensional holomorphic foliations of PC to those of algebraic varieties invariant by them. More precisely: if M is a connected complex manifold, a one-dimensional holomorphic foliation F of M is a morphism Φ : L −→ TM where L is a holomorphic line bundle on M . The singular set of F is the analytic subvariety sing(F) = {p ...

The present work describes a family of polynomial noninvertible maps of the plane shared within two open regions: (i) (denoted by Z0) each point having no real preimage, and (ii) (denoted by Z2) each point having two real preimages. The regions Z0, Z2 are separated by the critical curve LC, locus of points having two coincident preimages. Z2 is made up of two sheets (giving rise to a plane foli...

Wc compute te global multiplicity of a 1-dimensional foliation along an integral curve iii projective spaces. Wc give a bound in the way of Poincaré problem for complete intersection curves. In te projective plane, this bound give us a bound of te degree of non irreductible integral Curves in function of te degree of the foliation. O. INTRODUCTION Let jr be a foliation by lines in us take bomog...

These lecture notes were written to accompany a minicourse given at the School and Workshop on Dynamical Systems at IMPA (Rio de Janeiro), January 2006. Warning: These notes are unedited lecture notes and do contain errors! Proceed with caution... Let f : M → M be a (pointwise) partially hyperbolic diffeomor-phism. Recall what partially hyperbolic means. At every point in M , there exist tangen...

This terminology is explained by Bogomolov decomposition theorem which states that, up to a finite étale covering, each holomorphic symplectic manifold is a product of several irreducible ones and a torus. Let X be a holomorphic symplectic manifold with a holomorphic symplectic form ω. Let D be a smooth divisor on X. At each point of D, the restriction of ω to D has one-dimensional kernel. This...

We give a local proof of an index theorem for a Dirac-type operator that is invariant with respect to the action of a foliation groupoid G. If M denotes the space of units of G then the input is a G-equivariant fiber bundle P → M along with a G-invariant fiberwise Dirac-type operator D on P . The index theorem is a formula for the pairing of the index of D, as an element of a certain K-theory g...

It is shown how a pure background tensor formalism provides a concise but explicit and highly flexible machinery for the generalised curvature analysis of individual embedded surfaces and foliations such as arise in the theory of topological defects in cosmological and other physical contexts. The unified treatment provided here shows how the relevant extension of the Raychaudhuri identity is r...