Quasi-morphisms on contactomorphism groups and Grassmannians of 2-planes

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We construct a natural prequantization space over a monotone product of a toric manifold and an arbitrary number of complex Grassmannians of 2-planes in even-dimensional complex spaces, and prove that the universal cover of the identity component of the contactomorphism group of its total space carries a nonzero homogeneous quasi-morphism. The construction uses Givental’s nonlinear Maslov index and a reduction theorem for quasi-morphisms on contactomorphism groups previously established together with M. S. Borman. We explore applications to metrics on this group and to symplectic and contact rigidity. In particular we obtain a new proof that the quaternionic projective space HPn-1, naturally embedded in the Grassmannian G2(C2n) as a Lagrangian, cannot be displaced from the real part G2(R2n) by a Hamiltonian isotopy.

Original languageAmerican English
Pages (from-to)287-309
Number of pages23
JournalGeometriae Dedicata
Issue number1
StatePublished - 1 Aug 2020


  • Contact geometry
  • Contact rigidity
  • Contactomorhism group
  • Grassmannian
  • Quasi-morphism
  • Symplectic geometry
  • Symplectic rigidity

All Science Journal Classification (ASJC) codes

  • Geometry and Topology


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