On the Kauffman polynomial of an adequate link.
On the Kauffman-Harary conjecture for Alexander quandle colorings.
The Kauffman-Harary conjecture is a conjecture for Fox's colorings of alternating knots with prime determinants. We consider a conjecture for Alexander quandle colorings by referring to the Kauffman-Harary conjecture. We prove that this new conjecture is true for twist knots.
On the Mahler measure of Jones polynomials under twisting.
On the minimizers of the Möbius cross energy of links.
On the corresponding to bialgebras
On the placement problem of Reeb components.
On the Polynomials of Periodic Links.
On the residual properties of link groups.
On the Signature of a Link.
On the Signatures of Torus Knots
We study properties of the signature function of the torus knot . First we provide a very elementary proof of the formula for the integral of the signature over the circle. We also obtain a closed formula for the Tristram-Levine signature of a torus knot in terms of Dedekind sums.
On the Slice Genus of Knots.
On the slice genus of links.
On the stable equivalence of open books in three-manifolds.
On the structure of the centralizer of a braid
On transverse foliations
On unknotting operations of two-brigde knots.
On unkotting tunnels for knots.
Open 3-manifolds and branched coverings: a quick exposition.
Ordering Knots
Parity biquandle
We use crossing parity to construct a generalization of biquandles for virtual knots which we call parity biquandles. These structures include all biquandles as a standard example referred to as the even parity biquandle. We find all parity biquandles arising from the Alexander biquandle and quaternionic biquandles. For a particular construction named the z-parity Alexander biquandle we show that the associated polynomial yields a lower bound on the number of odd crossings as well as the total number...