Department of Mathematics
Indian Institute of Science
Bangalore 560 012
SEMINAR
Speaker |
: |
Dr. Eli Lebow |
Affiliation | : | NCBS, Bangalore. |
Subject Area |
: |
Mathematics
|
Venue |
: |
Lecture Hall - I, Dept of Mathematics
|
Time |
: |
4.00 pm
|
Date |
: |
April 4,2008 (Friday) |
Title |
: |
The Behavior of the Mordell-Weil Groups for an Elliptic Curve. |
Abstract | : |
Embedded contact homology is an invariant of contact 3-manifolds. ECH is given by the homology of a chain complex generated by certain collections of embedded closed Reeb orbits in the 3-manifold Y, with a differential that counts certain embedded pseudoholomorphic curves in Y x R. The result presented in this talk gives the ECH of T^2 bundles over S^1 whose monodromy A in SL_2(Z) is a hyperbolic matrix (or $-1$), where these manifolds are equipped with certain standard contact forms. The form of the answer is nearly independent of A, essentially depending only on whether the eigenvalues are positive or negative. This work extends the
results and methods of Hutchings and Sullivan (``Rounding corners of
polygons and the embedded contact homology of {$T\sp 3$}'', Geometry and
Topology, 2006) on the case Y=T^3. |