An integer valued bi-invariant metric on the group of contactomorphisms of R²n x S¹

2009/10/31 by Sheila Sandon · 1 citation
Mathematics · #math.SG #math.GT

paper · pdf

published as J. Topol. Anal. 2 (2010) 327--339 · 10 pages, final version

arxiv created 2011/10/21 · arxiv updated 2011/10/24

Abstract

In his 1992 article on generating functions Viterbo constructed a bi-invariant metric on the group of compactly supported Hamiltonian symplectomorphisms of R²n. Using the set-up of arXiv:0901.3112 we extend the Viterbo metric to the group of compactly supported contactomorphisms of R²n x S¹ isotopic to the identity. We also prove that the contactomorphism group is unbounded with respect to this metric.

Citations

• Contact Homology, Capacity and Non-Squeezing in R²n x S¹ via Generating Functions

Cited by

• On flat translated chains of contactomorphisms of ℝ²ⁿ⁺¹ and ℝ²ⁿ × S¹