41,158 research outputs found
Classical Knot Theory
This paper is a very brief introduction to knot theory. It describes knot
coloring by quandles, the fundamental group of a knot complement, and
handle-decompositions of knot complements.Comment: manuscript of paper in the journal Symmetry. There are some nice
pictures her
Twisted Virtual Biracks
This thesis will take a look at a branch of topology called knot theory. We will first look at what started the study of this field, classical knot theory. Knot invariants such as the Bracket polynomial and the Jones polynomial will be introduced and studied. We will then explore racks and biracks along with the axioms obtained from the Reidemeister moves. We will then move on to generalize classical knot theory to what is now known as virtual knot theory which was first introduced by Louis Kauffman. Finally, we take a look at a newer aspect of knot theory, twisted virtual knot theory and we defined new link invariants for twisted virtual biracks
Chebyshev Knots
A Chebyshev knot is a knot which admits a parametrization of the form where are
pairwise coprime, is the Chebyshev polynomial of degree and \phi
\in \RR . Chebyshev knots are non compact analogues of the classical Lissajous
knots. We show that there are infinitely many Chebyshev knots with
We also show that every knot is a Chebyshev knot.Comment: To appear in Journal of Knot Theory and Ramification
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