A New Route to the Interpretation of Hopf Invariant

• 来源期刊: 理论物理通讯(英文版)
• 年，卷（期）: 2008,（7）
• 页码范围: 53-58
• 页数: 6页
• 语种: 英文

摘要

We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mapping topological current theory.The main purpose of 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 R2n-1.For the sake of this purpose we introduce a topological tensor current,which can naturally deduce the (n- 1)-dimensional topological defect in R2n-1 space.If these (n- 1)-dimensional topological defects are closed oriented submanifolds of R2n-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.