AN INTEGER-VALUED BI-INVARIANT METRIC ON THE GROUP OF CONTACTOMORPHISMS OF ℝ²ⁿ × S¹

Abstract

In his article [23] on generating functions Viterbo constructed a bi-invariant metric on the group of compactly supported Hamiltonian symplectomorphisms of ℝ 2n . Using the setup of [18] we extend the Viterbo metric to the group Cont 0 c (ℝ 2n ×S 1 ) of compactly supported contactomorphisms of ℝ 2n ×S 1 isotopic to the identity. We also prove that Cont 0 c (ℝ 2n ×S 1 ) is unbounded with respect to this metric.