4 papers
Homotopy Type of the Space of Fibrations of the Three-sphere by Simple Closed Curves
Dennis Deturck, Ziqi Fang, Herman Gluck +4
We show that the moduli space of all smooth fibrations of a three-sphere by simple closed curves has the homotopy type of a disjoint union of a pair of two-spheres if the fibers ar…
On the homotopy type of the space of fiberings of by simple closed curves
Yi Wang, Jingye Yang
For most aspherical Seifert-fibered 3-manifolds , the space of Seifert fiberings is known to have contractible components. It is also known that the space of Hopf fiberi…
Deformation retraction of the group of strict contactomorphisms of the three-sphere to the unitary group
Dennis DeTurck, Herman Gluck, Leandro Lichtenfelz +3
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).
Great Circle Fibrations and Contact Structures on Odd-Dimensional Spheres
Herman Gluck, Jingye Yang
It is known that for every smooth great circle fibration of the 3-sphere, the distribution of tangent 2-planes orthogonal to the fibres is a contact structure, in fact a tight one,…