(t,s)-racks and their link invariants

Abstract

A (t,s)-rack is a rack structure defined on a module over the ring $\ddot{\Lambda }=\mathbb{Z}[t^{\pm 1},s]/(s^2-(1-t)s)$. We identify necessary and sufficient conditions for two $(t,s)$-racks to be isomorphic. We define enhancements of the rack counting invariant using the structure of (t,s)-racks and give some computations and examples. As an application, we use these enhanced invariants to obtain obstructions to knot ordering.

15 pages. Version 3 incorporates referee suggestions and a few corrections

References in corpus (2)

• Epimorphisms between 2-bridge link groups
• Upper bounds in the Ohtsuki-Riley-Sakuma partial order on 2-bridge knots

Cited by in corpus (1)

• Bikei, Involutory Biracks and unoriented link invariants