4 papers · 1 filter
Polynomial splittings of metabelian von Neumann rho-invariants
Se-Goo Kim, Taehee Kim
We show that if the connected sum of two knots with coprime Alexander polynomials has vanishing von Neumann rho-invariants associated with certain metabelian representations then s…
Polynomial splittings of Casson-Gordon invariants
Se-Goo Kim
In this paper we prove that the Casson-Gordon invariants of the connected sum of two knots split when the Alexander polynomials of the knots are coprime. As one application, for an…
Invertible knot concordances and prime knots
Se-Goo Kim
Kirby and Lickorish showed that every knot in the 3-sphere is concordant to a prime knot, equivalently, every concordance class contains a prime knot. We prove here that their resu…
Virtual Knot Groups
Se-Goo Kim
Virtual knots, defined by Kauffman, provide a natural generalization of classical knots. Most invariants of knots extend in a natural way to give invariants of virtual knots. In th…