If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching s...If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n展开更多
We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mappingtopological current theory.The main purpose of this paper is to present a new theoretical framework,which can di...We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mappingtopological current theory.The main purpose of this paper is to present a new theoretical framework,which can directlygive the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclideanspace 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 orientedsubmanifolds 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 linkingnumbers of the higher-dimensional knots can be constructed.展开更多
文摘If L is a link with two components and S1,S2…, Sn a switching sequence such that SnSn-1…S1L is unlinked, it is proved that lk（L） =∑i=1^nεi（L） and any link L can be transformed a n-twisting L~ by switching some crossings with the linking number：lk（L）=∑i=1^mεiC（EiL）＋n
基金National Natural Science Foundation of China and Cuiying Project of Lanzhou University
文摘We discuss an object from algebraic topology,Hopf invariant,and reinterpret it in terms of the φ-mappingtopological current theory.The main purpose of this paper is to present a new theoretical framework,which can directlygive the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclideanspace 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 orientedsubmanifolds 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 linkingnumbers of the higher-dimensional knots can be constructed.
