The (m,n)-Klein links are formed by altering the rectangular representation of an (m,n)-torus link. Using the braid representation of a (m,n)-Klein link, we generalize a previous braid word result and show that the (m, 2m)-Klein link can be expressed recursively. Applying braid permutations, we determine a formula for the number of components for an (m,n)-Klein link and classify the Klein links that are equivalent to knots.
Jennifer R. Bowen and John R. Ramsay, Department of Mathematics and Computer Science, The College of Wooster
Freund, David and Smith-Polderman, Sarah
"Klein Link Multiplicity and Recursion,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 17
, Article 8.
Available at: http://scholar.rose-hulman.edu/rhumj/vol17/iss2/8