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

TL;DR

This paper proves that the group of strict contactomorphisms of the standard tight contact structure on the three-sphere can be continuously shrunk to its U(2) subgroup, revealing a topological simplification.

Contribution

It establishes a deformation retraction of the strict contactomorphism group of S^3 onto U(2), a new topological relationship in contact geometry.

Findings

The strict contactomorphism group deformation retracts to U(2).

The result simplifies understanding of the group's topology.

Provides new insights into contactomorphism groups of S^3.

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).