An integer valued bi-invariant metric on the group of contactomorphisms of R^2n x S^1

Details An integer valued bi-invariant metric on the group of contactomorphisms of R^2n x S^1 An integer valued bi-invariant metric on the group of contactomorphisms of R^2n x S^1

2009-10-29

arxiv.org/abs/0910.5632v3

J. Topol. Anal. 2 (2010) 327--339

Mathematics

Symplectic Geometry

10 pages, final version

Scientific paper

In his 1992 article on generating functions Viterbo constructed a bi-invariant metric on the group of compactly supported Hamiltonian symplectomorphisms of R^2n. Using the set-up of arXiv:0901.3112 we extend the Viterbo metric to the group of compactly supported contactomorphisms of R^2n x S^1 isotopic to the identity. We also prove that the contactomorphism group is unbounded with respect to this metric.

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