32 citations · 55 across the 11 of their papers we have counts for
11 papers
Multiple points of view: The simultaneous crossing number for knots with doubly transvergent diagrams
Christoph Lamm, Michael Eisermann
The simultaneous crossing number is a new knot invariant which is defined for strongly invertible knots having diagrams with two orthogonal transvergent axes of strong inversions.…
Yang-Baxter deformations and rack cohomology
Michael Eisermann
Every rack provides a set-theoretic solution of the Yang-Baxter equation. This article examines the deformation theory of within the space of Yang-Baxter operators…
The Fundamental Theorem of Algebra made effective: an elementary real-algebraic proof via Sturm chains
Michael Eisermann
Sturm's theorem (1829/35) provides an elegant algorithm to count and locate the real roots of any real polynomial. In his residue calculus (1831/37) Cauchy extended Sturm's method…
The Jones polynomial of ribbon links
Michael Eisermann
For every n-component ribbon link L we prove that the Jones polynomial V(L) is divisible by the polynomial V(O^n) of the trivial link. This integrality property allows us to define…
A refined Jones polynomial for symmetric unions
Michael Eisermann, Christoph Lamm
Motivated by the study of ribbon knots we explore symmetric unions, a beautiful construction introduced by Kinoshita and Terasaka in 1957. For symmetric diagrams we develop a two-v…
Knot colouring polynomials
Michael Eisermann
This article introduces a natural extension of colouring numbers of knots, called colouring polynomials, and studies their relationship to Yang-Baxter invariants and quandle 2-cocy…