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.



 


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