An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that t...An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.展开更多
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
文摘An equivalent description for the torus knot is given in this paper, and the classification theorem of the torus knot is proved in an elementary method. Using the circular presentation of torus knot , we showed that the genus of the torus knot Kp,q is 1/2（p-1）（q-1） A knot called as bitorus knot is defined in the paper and showed . special that bitorus knot are all the connected sum of two torus knots.
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
