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

In his article [23] on generating functions Viterbo constructed a bi-invariant metric on the group of compactly supported Hamiltonian symplectomorphisms of ℝ2n. Using the setup of [18] we extend the Viterbo metric to the group Cont0 c (ℝ2n×S1) of compactly supported contactomorphisms of ℝ2n×S1 isotopic to the identity. We also prove that Cont0 c(ℝ2n×S1) is unbounded with respect to this metric.