Results 11 to 20 of about 45 (45)
Introduction to disoriented knot theory
Open Mathematics, 2018 This paper is an introduction to disoriented knot theory, which is a generalization of the oriented knot and link diagrams and an exposition of new ideas and constructions, including the basic definitions and concepts such as disoriented knot ...
Altıntaş İsmet
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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
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Skein modules of links in cylinders over surfaces
International Journal of Mathematics and Mathematical Sciences, Volume 32, Issue 9, Page 515-554, 2002., 2002 We define the Conway skein module 𝒞 (M) of ordered based links in a 3‐manifold M. This module gives rise to 𝒞 (M)‐valued invariants of usual links in M. We determine a basis of the ℤ[z]‐module 𝒞 (Σ × [0, 1])/Tor (𝒞 (Σ × [0, 1])), where Σ is the real projective plane or a surface with boundary. For cylinders over the Möbius strip or the projective plane,
Jens Lieberum
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Modeling repulsive forces on fibres via knot energies
Computational and Mathematical Biophysics, 2014 Modeling of repulsive forces is essential to the understanding of certain bio-physical processes, especially for the motion of DNA molecules. These kinds of phenomena seem to be driven by some sort of “energy” which especially prevents the molecules from
Blatt Simon, Reiter Philipp
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HEEGAARD FLOER HOMOLOGY AND RATIONAL CUSPIDAL CURVES
Forum of Mathematics, Sigma, 2014 We apply the methods of Heegaard Floer homology to identify topological properties of complex curves in $\mathbb{C}P^{2}$. As one application, we resolve an open conjecture that constrains the Alexander polynomial of the ...
MACIEJ BORODZIK, CHARLES LIVINGSTON
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About some infinite family of 2‐bridge knots and 3‐manifolds
International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 2, Page 95-108, 2000., 2000 We construct an infinite family of 3‐manifolds and show that these manifolds have cyclically presented fundamental groups and are cyclic branched coverings of the 3‐sphere branched over the 2‐bridge knots (ℓ + 1) 2 or (ℓ + 1) 1, that are the closure of the rational (2ℓ − 1)/(ℓ − 1)‐tangles or (2ℓ − 1)/ℓ‐tangles, respectively.
Yangkok Kim
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The classification of partially symmetric 3-braid links
Open Mathematics, 2015 We classify 3-braid links which are amphicheiral as unoriented links, including a new proof of Birman- Menasco’s result for the (orientedly) amphicheiral 3-braid links. Then we classify the partially invertible 3-braid links.
Stoimenov Alexander
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Characteristic polynomials of some weighted graph bundles and its application to links
International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 503-510, 1994., 1994 In this paper, we introduce weighted graph bundles and study their characteristic polynomial. In particular, we show that the characteristic polynomial of a weighted ‐bundles over a weighted graph G? can be expressed as a product of characteristic polynomials two weighted graphs whose underlying graphs are G As an application, we compute the signature ...
Moo Young Sohn, Jaeun Lee
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International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 3, Page 511-519, 1983., 1983 If we consider the set of manifolds that can be obtained by surgery on a fixed knot K, then we have an associated set of numbers corresponding to the Heegaard genus of these manifolds. It is known that there is an upper bound to this set of numbers.
Bradd Evans Clark
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The Heegaard genus of manifolds obtained by surgery on links and knots
International Journal of Mathematics and Mathematical Sciences, Volume 3, Issue 3, Page 583-589, 1980., 1980 Let L ⊂ S3 be a fixed link. It is shown that there exists an upper bound on the Heegaard genus of any manifold obtained by surgery on L. The tunnel number of L, T(L), is defined and used as an upper bound. If K′ is a double of the knot K, it is shown that T(K′) ≤ T(K) + 1.
Bradd Clark
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