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To Manfredo do Carmo in friendship and admiration, on his 80 th birthday Abstract. 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 by the pairwise linking numbers p, q and r of the components, and by the residue class of one(More)
The rate of decrease of gallstone diameter appeared to be linear with oral bile acid treatment time, as estimated by inspection of graphic data of individual patient serial oral cholecystograms. A theoretical basis for this model was derived. The hypothesis of diameter decrease proportional to treatment time was tested with data from 223 patients with(More)
The writhing number of a curve in Euclidean 3-space, introduced by C˘ alug˘ areanu (1959-61) and named by Fuller (1971), is the standard measure of the extent to which the curve wraps and coils around itself; it has proved its importance for molecular biologists in the study of knotted duplex DNA and of the enzymes which affect it. The helicity of a vector(More)
The helicity of a smooth vector field defined on a domain in 3-space is the standard measure of the extent to which the field lines wrap and coil around one another; it plays important roles in fluid mechanics, magnetohy-drodynamics and plasma physics. In this report we show how the relation between energy and helicity of a vector field is influenced by the(More)
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. To each three-component link in Euclidean 3–space, we associate a generalized Gauss map from the 3–torus to the 2–sphere, and show that the pairwise linking numbers and Milnor triple(More)