2013/08/31 by Matthew Strom Borman, Frol Zapolsky · 1 citation
Mathematics · #math.SG #msc:53D35 #msc:53D12 #msc:53D20
paper · pdf · doi:10.2140/gt.2015.19.365
published as Geom. Topol. 19 (2015) 365-411 · 40 pages, 1 figure; v3: added proof of C^0 continuity, minor corrections. To appear in Geometry & Topology
arxiv created 2014/04/26 · arxiv updated 2015/05/27
We build homogeneous quasi-morphisms on the universal cover of the contactomorphism group for certain prequantizations of monotone symplectic toric manifolds. This is done using Givental's nonlinear Maslov index and a contact reduction technique for quasi-morphisms. We show how these quasi-morphisms lead to a hierarchy of rigid subsets of contact manifolds. We also show that the nonlinear Maslov index has a vanishing property, which plays a key role in our proofs. Finally we present applications to orderability of contact manifolds and Sandon-type metrics on contactomorphism groups.