(t,s)-racks and their link invariants

Details (t,s)-racks and their link invariants (t,s)-racks and their link invariants

2010-11-24

arxiv.org/abs/1011.5455v3

Mathematics

Geometric Topology

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

Scientific paper

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.

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