Inner topological structure of Hopf invariant

Abstract

In light of $\varphi$-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.

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

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Cited by in corpus (5)

• Stationary ring solitons in field theory - knots and vortons
• Hopf characterization of two-dimensional Floquet topological insulators
• Topological Aspect of Knotted Vortex Filaments in Excitable Media
• Knotted Topological Phase Singularities of Electromagnetic Field
• The branch processes of vortex filaments and Hopf Invariant Constraint on Scroll Wave