Mathematics > Symplectic Geometry
[Submitted on 26 Nov 2007 (v1), last revised 18 Jan 2009 (this version, v2)]
Title:Loops in the Hamiltonian group: a survey
View PDFAbstract: 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).
Submission history
From: Dusa McDuff [view email][v1] Mon, 26 Nov 2007 19:39:28 UTC (30 KB)
[v2] Sun, 18 Jan 2009 13:45:36 UTC (30 KB)
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