40 citations · 90 across the 13 of their papers we have counts for
9 papers · 1 filter
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…
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…
Linking, twisting, writhing and helicity on the 3-sphere and in hyperbolic 3-space
Dennis DeTurck, Herman Gluck
We obtain explicit, isometry-invariant integral formulas for twisting, writhing and helicity, and prove the theorem LINK = TWIST + WRITHE on the 3-sphere and in hyperbolic 3-space.…
Triple linking numbers, ambiguous Hopf invariants and integral formulas for three-component links
Dennis DeTurck, Herman Gluck, Rafal Komendarczyk +3
Three-component links in the 3-dimensional sphere were classified up to link homotopy by John Milnor in his senior thesis, published in 1954. A complete set of invariants is given…