2108.08961Aug 20, 2021Expanded 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
Deformation retraction of the group of strict contactomorphisms of the three-sphere to the unitary group
Dennis DeTurck, Herman Gluck, Leandro Lichtenfelz, Mona Merling, Jingye Yang, Yi Wang
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).