Recursion in Topological Invariants of Twist and Rational Knot Exteriors
Christian Gorski · Rose-Hulman Scholar (Rose–Hulman Institute of Technology) · 2016
We calculate explicit presentations for the knot group of twist knots, utilizing a recursive relation derived from the Wirtinger presentation.We also present a method for building rational knot exteriors by attaching two-handles to (S 2 -::)×I, the four-punctured sphere times an interval, and give an explicit algorithm for calculating the attaching curve for the two-handles in terms of the basis of the Kauffman bracket skein module of (S 2 -::) × I.