A New Route to the Interpretation of Hopf Invariant

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dc.creatorRen, Ji-rong
dc.creatorLi, Ran
dc.creatorDuan, Yi-shi
dc.date2006-07-01
dc.date2007-10-19
dc.date.accessioned2026-07-07T12:12:32Z
dc.date.available2026-07-07T12:12:32Z
dc.descriptionWe discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the $ϕ$-mapping topological current theory. The main purpose in this paper is to present a new theoretical framework which can directly give the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclidean space $R^{2n-1}$. For the sake of this purpose we introduce a topological tensor current which can naturally deduce the $(n-1)$ dimensional topological defect in $R^{2n-1}$ space. If these $(n-1)$ dimensional topological defects are closed oriented submanifolds of $R^{2n-1}$, they are just the $(n-1)$ dimensional knots. The linking number of these knots is well defined. Using the inner structure of the topological tensor current, the relationship between Hopf invariant and the linking numbers of the higher dimensional knots can be constructed.
dc.description13 pages, no figures, Accepted by Commun. Theor. Phys. (Beijing, China)
dc.identifierhttps://arxiv.org/abs/math-ph/0607001
dc.identifierhttp://arxiv.org/abs/math-ph/0607001
dc.identifierCommun. Theor. Phys. (Beijing, China) 50 (2008) pp. 53?C58
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/210572
dc.subjectMathematical Physics
dc.titleA New Route to the Interpretation of Hopf Invariant
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