The symplectic fiber sum construction is one of the few surgery technique available to construct new symplectic manifolds out of olds ones. The goal of the talk is to explain the construction and, if time permits, to give some applications .
Luttinger's surgery and complex structures on $T^2\times D^2$.
October 09, 14:30 - 15:30, MC 107
I will describe a result by Eliashberg and Polterovich
that allows to construct a family $J_n$ of complex structures
on $T^2\times D^2$ with strictly pseudoconvex boundary which are
biholomorphically equivalent and homotopic through complex structures
but not homotopic through complex structures with strictly pseudoconvex
boundary. Note: $T^2\times D^2$ denotes the product of the 2-torus
and the closed unit disk in $R^2$. The proof is based on the Lagrangian
surgery method of K. Luttinger.
Gromov's celebrated "Nonsqueezing Theorem" states that one cannot "squeeze" a symplectic ball into a thin cylinder using a symplectic transformation. This shows that symplectic diffeomorphisms are more rigid that volume preserving ones, and that there exists a notion of "size" peculiar to symplectic object. In this talk, I will explain the linear version of this theorem.
Everyone interested in symplectic geometry / topology is welcome.
The University of Western Ontario
