Examples on Polynomial Invariants of Knots and Links.
Taizo Kanenobu (1986)
Mathematische Annalen
Similarity:
Taizo Kanenobu (1986)
Mathematische Annalen
Similarity:
Moshe Cohen, Oliver T. Dasbach, Heather M. Russell (2014)
Fundamenta Mathematicae
Similarity:
We develop a dimer model for the Alexander polynomial of a knot. This recovers Kauffman's state sum model for the Alexander polynomial using the language of dimers. By providing some additional structure we are able to extend this model to give a state sum formula for the twisted Alexander polynomial of a knot depending on a representation of the knot group.
Teruaki Kitano, Takayuki Morifuji (2005)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
We prove that Wada’s twisted Alexander polynomial of a knot group associated to any nonabelian -representation is a polynomial. As a corollary, we show that it is always a monic polynomial of degree for a fibered knot of genus .
Stoimenow, Alexander (2000)
Experimental Mathematics
Similarity:
Kitano, Teruaki, Suzuki, Masaaki, Wada, Masaaki (2005)
Algebraic & Geometric Topology
Similarity:
Anh T. Tran (2015)
Fundamenta Mathematicae
Similarity:
We study the AJ conjecture that relates the A-polynomial and the colored Jones polynomial of a knot in S³. We confirm the AJ conjecture for (r,2)-cables of the m-twist knot, for all odd integers r satisfying ⎧ (r+8)(r−8m) > 0 if m > 0, ⎨ ⎩ r(r+8m−4) > 0 if m < 0.
Aaron Kaestner, Louis H. Kauffman (2014)
Banach Center Publications
Similarity:
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...
Shin Satoh, Kenta Taniguchi (2014)
Fundamenta Mathematicae
Similarity:
Kauffman introduced a fundamental invariant of a virtual knot called the odd writhe. There are several generalizations of the odd writhe, such as the index polynomial and the odd writhe polynomial. In this paper, we define the n-writhe for each non-zero integer n, which unifies these invariants, and study various properties of the n-writhe.
Nafaa Chbili (2003)
Annales de la Faculté des sciences de Toulouse : Mathématiques
Similarity:
Dunfield, Nathan M., Garoufalidis, Stavros (2004)
Algebraic & Geometric Topology
Similarity:
G. Ananda Swarup (1971)
Mathematische Zeitschrift
Similarity:
Tazio Kanenobu (1989)
Mathematische Annalen
Similarity:
Prabhakar Madeti, Rama Mishra (2006)
Fundamenta Mathematicae
Similarity:
We discuss polynomial representations for 2-bridge knots and determine the minimal degree sequence for all such knots. We apply the connection between rational tangles and 2-bridge knots.