5 papers · 1 filter
Order in the concordance group and Heegaard Floer homology
Stanislav Jabuka, Swatee Naik
We use the Heegaard-Floer homology correction terms defined by Ozsváth--Szabó to formulate a new obstruction for a knot to be of finite order in the smooth concordance group. This…
Ozsvath-Szabo and Rasmussen invariants of doubled knots
Charles Livingston, Swatee Naik
Let νbe any integer-valued additive knot invariant that bounds the smooth 4-genus of a knot K, |ν(K)| <= g_4(K), and determines the 4-ball genus of positive torus knots, ν(T_{p,q})…
Twisted Alexander polynomials of periodic knots
Jonathan A Hillman, Charles Livingston, Swatee Naik
Murasugi discovered two criteria that must be satisfied by the Alexander polynomial of a periodic knot. We generalize these to the case of twisted Alexander polynomials. Examples d…
A move on diagrams that generates S-equivalence of knots
Swatee Naik, Theodore Stanford
Two knots in three-space are S-equivalent if they are indistinguishable by Seifert matrices. We show that S-equivalence is generated by the doubled-delta move on knot diagrams. It…
Obstructing 4-torsion in the classical knot concordance group
Charles Livingston, Swatee Naik
We prove that if the order of the first homology of the 2-fold branched cover of a knot K in the 3-sphere is given by pm where p is a prime congruent to 3 mod 4 and gcd(p,m) =1, th…