arXiv research

Invariants for colored links found, with topological protection of certain knots.

A combinatorial presentation of closed orientable 3-manifolds as bi-tricolored links is given together with two versions of a calculus via moves to manipulate bi-tricolored links without changing the represented manifold. That is, we provide a finite set of moves sufficient to relate any two manifestations of the same …

S. Nelson, M. Orrison, V. Rivera {\cite{S}} modified Kauffman's construction of bracket. Their invariant $Φ^β_X$ takes value in a finite ring $Z_2[t]/(1+t+t^3)$. In this paper, the author generalizes this invariant. The new invariant takes value in a polynomial ring. Furthermore, for a tricolorable link diagram, the au…

This paper shows all elements in the 3-colorable subgroup of Thompson's group give 3-colorable links.

Quotients of Gordian and H(2)-Gordian graphs are hyperbolic.

We extend the notion of link colorings with values in an Alexander quandle to link colorings with values in a module $M$ over the Laurent polynomial ring $Λ_μ=\mathbb{Z}[t_1^{\pm1},\dots,t_μ^{\pm1}]$. If $D$ is a diagram of a link $L$ with $μ$ components, then the colorings of $D$ with values in $M$ form a $Λ_μ$-module…