arXiv subjects

Khaled Bataineh

Publications and source records attributed to Khaled Bataineh.

3 recordsLinked to original sources

arXiv2018

Generating sets of Reidemeister moves of oriented singular links and quandles

We give a generating set of the generalized Reidemeister moves for oriented singular links. We use it to introduce an algebraic structure arising from the study of oriented singular knots. We give some examples, including some non-isomorphic families of such structures over non-abelian groups. We show that the set of colorings of a singular knot by this new structure is an invariant of oriented singular knots and use it to distinguish some singular links.

math.GT↗

arXiv2018

On Rational Knots and Links in the Solid Torus

We introduce the notion of rational links in the solid torus. We show that rational links in the solid torus are fully characterized by rational tangles, and hence by the continued fraction of the rational tangle. Furthermore, we generalize this by giving an infinite family of ambient isotopy invariants of colored diagrams in the Kauffman bracket skein module of an oriented surface.

math.GT↗

arXiv2016

The Colored Jones Polynomial of Singular Knots

We generalize the colored Jones polynomial to $4$-valent graphs. This generalization is given as a sequence of invariants in which the first term is a one variable specialization of the Kauffman-Vogel polynomial. We use the invariant we construct to give a sequence of singular braid group representations.

math.GT↗