Introduction to Contact Topology (Fall 2014)
Location and time:
There will be three sets of hand-in problems. They will count for 50 percent of your
grade. At the end of the course there will be an oral exam.
The standard basic notion that are tought in the first course on Differential Geometry, such as:
the notion of manifold, smooth maps, immersions and submersions, tangent vectors, Lie derivatives along
vector fields, the flow of a tangent vector, the tangent space (and bundle), the definition of differential
forms, DeRham operator (and hopefully the definition of DeRham cohomology).
Please do all the homework exercises. The hand-in problems will be also posted on this page.
The schedule week by week (here we will try to add, after each lecture, a description of what was
discussed in the lectures):
Aim/content of the course:
Contact topology originated more than three centuries ago in the work of Huygens, Hamilton
and Jacobi on geometric optics. More recently, it has developed into a very active field
of research, with profound connections to low-dimensional topology, symplectic topology,
and Hamiltonian dynamics.
A contact structure is a geometric structure on a smooth manifold, defined by a one-form
which satisfies a condition called "maximal non-integrability". Examples of manifolds
admitting a contact structure are: odd-dimensional Euclidean spaces, spheres, and tori.
The main aim of this course is to cover the basic notions of contact topology: contact
structures, characteristic foliations, families of contact structures and Moser's method,
the tight-overtwisted dichotomy. We also hope to address topics like special knots in
contact manifolds, convex surfaces and open book decompositions.
The main reference for this course is:
Good references for the background material are:
Last update: 27-11-2014