Symplectic convexity in low-dimensional topology

Symplectic Convexity in Low Dimensional Topology

In this paper we will survey the the various forms of convexity in symplectic geometry, paying particular attention to applications of convexity in low dimensional topology.

Parameterized Morse theory in low-dimensional and symplectic topology

The first part of the talk will be a quick survey on the homotopy type of the group of Diffeomorphisms of a 3-manifold. Pioneering work was done by Hatcher and Ivanov in the late 70s and early 80s, computing this for Haken 3-manifolds and famously the Smale conjecture. Following Thurston, the natural question is whether Diff is homotopy equivalent to the group of isometries, for geometric 3-man...

Problems in Low-dimensional Topology

Four-dimensional topology is in an unsettled state: a great deal is known, but the largest-scale patterns and basic unifying themes are not yet clear. Kirby has recently completed a massive review of low-dimensional problems [Kirby], and many of the results assembled there are complicated and incomplete. In this paper the focus is on a shorter list of \tool" questions, whose solution could unif...

Low - dimensional Topology 57

Metric convexity in the symplectic category

We introduce an extension of the standard Local-to-Global Principle used in the proof of the convexity theorems for the momentum map to handle closed maps that take values in a length metric space. This extension is used to study the convexity properties of the cylinder valued momentum map introduced by Condevaux, Dazord, and Molino in [8] and allows us to obtain the most general convexity stat...