(t,s)-racks and their link invariants

الأصل · EN

A (t,s)-rack is a rack structure defined on a module over the ring Λ=Z[t± ¹,s]/(s²-(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.