A natural framing of knots.
A natural series for the natural logarithm.
A new algorithm for recognizing the unknot.
A new criterion for knots with free periods
A New Knot Invariant.
A new proof of Markov's braid theorem
The purpose of this paper is to introduce a new proof of Markov's braid theorem, in terms of Seifert circles and Reidemeister moves. This means that the proof will be of combinatorial and essentially 2-dimensional nature. One characteristic feature of our approach is that nowhere in the proof will we use or refer to the braid axis. This allows for greater flexibility in various transformations of the diagrams considered. Other proofs of Markov's theorem can be found in [2], [3], [4] and [5].
A new technique for the link slice problem.
A Note on 2-fold Branched Covering Spaces of S3.
A note on a multi-variable polynomial link invariant
A note on a recursive formula of the Arf-Kervaire invariant.
A note on irreducible Heegaard diagrams.
A Note on Link Complements and Arithmetic Groups.
A Note on the Rational Cuspidal Curves
In this short note we give an elementary combinatorial argument, showing that the conjecture of J. Fernández de Bobadilla, I. Luengo-Velasco, A. Melle-Hernández and A. Némethi [Proc. London Math. Soc. 92 (2006), 99-138, Conjecture 1] follows from Theorem 5.4 of Brodzik and Livingston [arXiv:1304.1062] in the case of rational cuspidal curves with two critical points.
A note on unlinking numbers of Montesinos links.
Let K (resp. L) be a Montesinos knot (resp. link) with at least four branches. Then we show the unknotting number (resp. unlinking number) of K (resp. L) is greater than 1.
A partial order in the knot table.
A polynomial invariant for unoriented knots and links.
A polynomial invariant of rational homology 3-spheres.
A proof of Tait’s Conjecture on prime alternating achiral knots
In this paper we are interested in symmetries of alternating knots, more precisely in those related to achirality. We call the following statement Tait’s Conjecture on alternating achiral knots:Let be a prime alternating achiral knot. Then there exists a minimal projection of in and an involution such that:1) reverses the orientation of ;2) ;3) ;4) has two fixed points on and hence reverses the orientation of .The purpose of this paper is to prove this statement.For the historical...
A rational noncommutative invariant of boundary links.
A search method for thin positions of links.