Quasimorphisms on contactomorphism groups and contact rigidity

Borman, Matthew Strom¹ ; Zapolsky, Frol²

¹ Department of Mathematics, Stanford University, Building 380, Stanford, CA 94305, USA
² Department of Mathematics, University of Haifa, Mount Carmel, Haifa 31905, Israel

Geometry & topology, Tome 19 (2015) no. 1, pp. 365-411.

Résumé

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.

Détail

DOI : 10.2140/gt.2015.19.365

Classification : 53D35, 53D12, 53D20
Keywords: quasimorphism, contactomorphism, contact rigidity, nonlinear Maslov index, prequantization, toric

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