Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr. David Farris, |
Affiliation | : | U.C. Berkeley |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
11.00 am
|
Date |
: |
Dec 16,2008 (Tuesday) |
Title |
: |
The Embedded Contact Homology of Circle Bundles over Riemann Surfaces |
Abstract | : |
Embedded contact homology (ECH)
is an invariant of three-manifolds due to Hutchings, Sullivan, and Taubes.
It uses a contact structure on a three-manifold to produce an invariant of
the underlying topological manifold. The invariant is the homology of a
chain complex generated by certain closed orbits of the Reeb vector field
(of interest in classical dynamics), whose differential counts certain
holomorphic curves in the symplectization of the contact three-manifold. Few
nontrivial examples of ECH have been computed. In this talk, I will give
some background and context on ECH and then describe the computation of the
ECH of circle bundles over Riemann surfaces, in which the relevant
holomorphic curves are actually meromorphic sections of complex line
bundles.
|