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Generalized Gauss maps and integrals for three-component links: Toward higher helicities for magnetic fields and fluid flows

2013
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Journal of Mathematical Physics
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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 flows and magnetic fields. To each three-component link in Euclidean 3-space, we associate a geometrically natural generalized Gauss map from the 3-torus to the 2-sphere, and show that the pairwise linking numbers and Milnor triple linking number that classify the link up to link homotopy correspond to the Pontryagin

doi:10.1063/1.4774172
fatcat:yfmplsdtvnaprdo6g5o7wxvcmi