40 citations · 90 across the 13 of their papers we have counts for
13 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).
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…
Generalized Gauss maps and integrals for three-component links: toward higher helicities for magnetic fields and fluid flows, Part 2
Dennis DeTurck, Herman Gluck, Rafal Komendarczyk +4
We describe a new approach to triple linking invariants and integrals, aiming for a simpler, wider and more natural applicability to the search for higher order helicities of fluid…
Pontryagin invariants and integral formulas for Milnor's triple linking number
Dennis DeTurck, Herman Gluck, Rafal Komendarczyk +3
To each three-component link in the 3-sphere, we associate a geometrically natural characteristic map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers a…
Lipschitz minimality of Hopf fibrations and Hopf vector fields
Dennis DeTurck, Herman Gluck, Peter A. Storm
Given a Hopf fibration of a round sphere by parallel great subspheres, we prove that the projection map to the base space is, up to isometries of domain and range, the unique Lipsc…