Deformation retraction of the group of strict contactomorphisms of the three-sphere to the unitary group

Abstract

We prove that the group of strict contactomorphisms of the standard tight contact structure on the three-sphere deformation retracts to its unitary subgroup U(2).

arXiv commentExpanded both content and references. Separated into two parts. Part 1 is a more detailed proof of our new result of the deformation retraction of the group of strict contactomorphisms on the three-sphere. Part 2 gives a self-contained treatment and proofs of existing results scattered among several papers in the literature on the Fréchet bundle structure of the group of strict contactomorphisms