Affordable Access

Loops in the Hamiltonian group: a survey

Authors
  • McDuff, Dusa
Type
Preprint
Publication Date
Jan 18, 2009
Submission Date
Nov 26, 2007
Source
arXiv
License
Yellow
External links

Abstract

This note describes some recent results about the homotopy properties of Hamiltonian loops in various manifolds, including toric manifolds and one point blow ups. We describe conditions under which a circle action does not contract in the Hamiltonian group, and construct an example of a loop $\ga$ of diffeomorphisms of a symplectic manifold M with the property that none of the loops smoothly isotopic to $\ga$ preserve any symplectic form on M. We also discuss some new conditions under which the Hamiltonian group has infinite Hofer diameter. Some of the methods used are classical (Weinstein's action homomorphism and volume calculations), while others use quantum methods (the Seidel representation and spectral invariants).

Report this publication

Statistics

Seen <100 times