40 citations · 95 across the 16 of their papers we have counts for
16 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…
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,…
Great circle fibrations and contact structures on the 3-sphere
Herman Gluck
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 fa…
Making matrices better: Geometry and topology of polar and singular value decomposition
Dennis DeTurck, Amora Elsaify, Herman Gluck +4
Our goal here is to see the space of matrices of a given size from a geometric and topological perspective, with emphasis on the families of various ranks and how they fit together…
Deformation and Extension of Fibrations of Spheres by Great Circles
Patricia Cahn, Herman Gluck, Haggai Nuchi
In a 1983 paper with Frank Warner, we proved that the space of all great circle fibrations of the 3-sphere S^3 deformation retracts to the subspace of Hopf fibrations, and so has t…