2006/11/10 by Gabi Ben Simon, Simon, Gabi Ben
Mathematics · Physics and Astronomy · #37K65 53D10 53D12 53D50 #FOS: Mathematics #FOS: Physical sciences #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG) #math-ph #math.MP #math.SG #msc:37K65 #msc:53D10 #msc:53D12 #msc:53D50
paper · pdf · doi:10.48550/arxiv.math/0611320
29 pages 2 figures. submitted for publication
openalex publication_date 2006/11/10 · arxiv created 2006/11/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we find connection between the Hofer's metric of the group of Hamiltonian diffeomorphisms of a closed symplectic manifold, with an integral symplectic form, and the geometry, defined in a paper by Eliashberg and Polterovich, of the quantomorphisms group of its prequantization manifold. This gives two main results: First, we calculate, partly, the geometry of the quantomorphisms groups of a prequantization manifolds of an integral symplectic manifold which admits certain Lagrangian foliation. Second, for every prequantization manifold we give a formula for the distance between a point and a distinguished curve in the metric space associated to its group of quantomorphisms. Moreover, our first result is a full computation of the geometry related to the symplectic linear group which can be considered as a subgroup of the contactomorphisms group of suitable prequantization manifolds of the complex projective space. In the course of the proof we use in an essential way the Maslov quasimorphism.