Codimension One Foliations of 3-Manifolds

Resumen:

A k-dimensional foliation of an n-manifold is a decomposition of the manifold into k-manifolds, called leaves, such that locally (that is, on charts for some choice of atlas) this decomposition gives a product R^k×R^n-k. One thus has a globally defined notion of ``horizontal'' motion (motion restricted to a particular leaf) and ``vertical'' motion (motion always transverse to the leaves) through the manifold. This extra structure, when present, can be very useful in revealing properties of the manifold.

Foliations arose originally in the study of solutions to differential equations. Current research includes the study of the properties and structure of foliations satisfying a variety of naturally arising constraints, the investigation of topological, algebraic and geometric consequences arising from the existence of such foliations, and the search for interesting constructions. In this talk, I will discuss codimension-one foliations of 3-manifolds, touching on each of these three areas of current research.

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