Results 11 to 20 of about 1,468 (49)
On the Reidemeister torsion of rational homology spheres
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 1, Page 11-17, 2001., 2001 We prove that the Modℤ reduction of the Reidemeister torsion of a rational homology 3‐sphere is naturally a ℚ/ℤ‐valued quadratic function uniquely determined by a ℚ/ℤ‐constant and the linking form.
Liviu I. Nicolaescu
wiley +1 more source
A study about the Tutte polynomials of benzenoid chains
Topological Algebra and its Applications, 2017 The Tutte polynomials for signed graphs were introduced by Kauffman. In 2012, Fath-Tabar, Gholam-Rezaeı and Ashrafı presented a formula for computing Tutte polynomial of a benzenoid chain. From this point on, we have also calculated the Tutte polynomials
Sahin Abdulgani
doaj +1 more source
Upper bound on lattice stick number of knots [PDF]
, 2012 The lattice stick number $s_L(K)$ of a knot $K$ is defined to be the minimal number of straight line segments required to construct a stick presentation of $K$ in the cubic lattice.
Adams +3 more
core +1 more source
Quandle and Biquandle Homology Calculation in R
Journal of Open Research Software, 2018 In knot theory several knot invariants have been found over the last decades. This paper concerns itself with invariants of several of those invariants, namely the Homology of racks, quandles, biracks and biquandles.
Roger Fenn, Ansgar Wenzel
doaj +1 more source
Skein Algebras of the solid torus and symmetric spatial graphs [PDF]
, 2006 We use the topological invariant of spatial graphs introduced by S. Yamada to find necessary conditions for a spatial graph to be periodic with a prime period. The proof of the main result is based on computing the Yamada skein algebra of the solid torus
Chbili, Nafaa
core +2 more sources
Roots of torsion polynomials and dominations [PDF]
, 2008 We show that the nonzero roots of the torsion polynomials associated to the infinite cyclic covers of a given compact, connected, orientable 3-manifold M are contained in a compact part of the complex plane a priori determined by M.
Boileau, Michel +2 more
core +5 more sources
Mp-small summands increase knot width
, 2004 Scharlemann and Schultens have shown that for any pair of knots K_1 and K_2, w(K_1 # K_2) is greater than or equal to max{w(K_1),w(K_2)}. Scharlemann and Thompson have given a scheme for possible examples where equality holds.
Gabai +3 more
core +1 more source
Knot Floer homology and Seifert surfaces
, 2007 Let K be a knot in S^3 of genus g and let n>0. We show that if rk HFK(K,g) < 2^{n+1} (where HFK denotes knot Floer homology), in particular if K is an alternating knot such that the leading coefficient a_g of its Alexander polynomial satisfies |a_g|
Andras Juhasz, Gabai, Kakimizu, Kakimizu
core +3 more sources
Burnside obstructions to the Montesinos-Nakanishi 3-move conjecture
, 2002 Yasutaka Nakanishi asked in 1981 whether a 3-move is an unknotting operation. In Kirby's problem list, this question is called `The Montesinos-Nakanishi 3-move conjecture'.
Burnside +6 more
core +1 more source
Upper bound on the total number of knot $n$-mosaics
, 2014 Lomonaco and Kauffman introduced a knot mosaic system to give a definition of a quantum knot system which can be viewed as a blueprint for the construction of an actual physical quantum system.
Hong, Kyungpyo +3 more
core +1 more source