Great circle fibrations and contact structures on the 3-sphere
Differential Geometry
2018-02-13 v1 Algebraic Topology
Geometric Topology
Symplectic Geometry
Abstract
Given any smooth fibration of the unit 3-sphere by great circles, we show that the distribution of 2-planes orthogonal to the great circle fibres is a tight contact structure, a fact well known in the special case of the Hopf fibrations. The proof expresses hypothesis and conclusion as differential inequalities involving functions on disks transverse to the fibres, and shows that one inequality implies the other.
Cite
@article{arxiv.1802.03797,
title = {Great circle fibrations and contact structures on the 3-sphere},
author = {Herman Gluck},
journal= {arXiv preprint arXiv:1802.03797},
year = {2018}
}
Comments
19 pages, 5 figures, Differential Geometry, Contact Geometry, Manifolds and Cell Complexes