TY - JOUR
T1 - Quasimorphisms on contactomorphism groups and contact rigidity
AU - Borman, Matthew Strom
AU - Zapolsky, Frol
PY - 2015/2/27
Y1 - 2015/2/27
N2 - We build homogeneous quasimorphisms 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 quasimorphisms. We show how these quasimorphisms 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.
AB - We build homogeneous quasimorphisms 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 quasimorphisms. We show how these quasimorphisms 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.
UR - http://www.scopus.com/inward/record.url?scp=84924334431&partnerID=8YFLogxK
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U2 - 10.2140/gt.2015.19.365
DO - 10.2140/gt.2015.19.365
M3 - Article
AN - SCOPUS:84924334431
VL - 19
SP - 365
EP - 411
JO - Geometry and Topology
JF - Geometry and Topology
SN - 1364-0380
IS - 1
ER -