Achirality of knots and links
Boju Jiang, Xiao-Song Lin, Shicheng Wang, Ying-Qing Wu
Abstract
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 S3. For example, we show that the twisted Whitehead double of a knot is achiral if and only if the double is the unknot or the figure eight knot, and we show that all non-trivial links with ≤9 crossings are not achiral except the Borromean rings. A simple procedure for calculating the η-function is given in terms of a crossing change formula and its initial values.
Create a lesson
Related papers
Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
Nancy Scherich, Nathaniel Song
The flip symmetry on Khovanov-Rozansky homology
Hongjian Yang
Families of knots that cannot be made Legendrian parametrically
Javier Martínez-Aguinaga
Branched real projective structures on surfaces and geometrisation of representations
Gianluca Faraco, Nicholas Rungi
Generating the twist subgroup of the level 2 mapping class group of a non-orientable closed surface
Ryoma Kobayashi
H-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
Sungkyung Kang, JungHwan Park, Masaki Taniguchi