Inner topological structure of Hopf invariant

Details Inner topological structure of Hopf invariant Inner topological structure of Hopf invariant

2007-05-30

arxiv.org/abs/0705.4337v1

J.Math.Phys.48:073502,2007

Physics

Mathematical Physics

13pages, no figure. Accepted by J.Math.Phys

Scientific paper

10.1063/1.2747614

In light of $\phi$-mapping topological current theory, the inner topological structure of Hopf invariant is investigated. It is revealed that Hopf invariant is just the winding number of Gauss mapping. According to the inner structure of topological current, a precise expression for Hopf invariant is also presented. It is the total sum of all the self-linking and all the linking numbers of the knot family.

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