2 citations · 5 across the 5 of their papers we have counts for
11 papers · 1 filter
A New Way to Tabulate Knots
Lisa Hernandez, Xiao-Song Lin
We introduce a new way to tabulate knots by representing knot diagrams using a pair of planar trees. This pair of trees have their edges labeled by integers, they have no valence 2…
On n-punctured ball tangles
Jae-Wook Chung, Xiao-Song Lin
We consider a class of topological objects in the 3-sphere which will be called {\it -punctured ball tangles}. Using the Kauffman bracket at , an invariant for…
Knot adjacency and satellites
Efstratia Kalfagianni, Xiao-Song Lin
A knot K is called n-adjacent to the unknot, if K admits a projection containing n generalized crossings such that changing any m (no larger than n) of them yields a projection of…
Link-homotopy Invariants of Finite Type
Xiao-Song Lin
An explicit polynomial in the linking numbers and Milnor's triple linking numbers on six component links is shown to be a well-defined finite type link-homotopy i…
Vassiliev invariants and the cubical knot complex
Ilya Kofman, Xiao-Song Lin
We construct a cubical CW-complex CK(M^3) whose rational cohomology algebra contains Vassiliev invariants of knots in the 3-manifold M^3. We construct \bar{CK}(R^3) by attaching ce…
Achirality of knots and links
Boju Jiang, Xiao-Song Lin, Shicheng Wang +1
We will develop various methods, some are of geometric nature and some are of algebraic nature, to detect the various achiralities of knots and links in . For example, we show…