12 research outputs found
Mock Alexander Polynomials
In this paper, we construct mock Alexander polynomials for starred links and
linkoids in surfaces. These polynomials are defined as specific sums over
states of link or linkoid diagrams that satisfy , where denotes the
number of regions and denotes the number of crossings of diagrams
Graphoids
We study invariants of virtual graphoids, which are virtual spatial graph
diagrams with two distinguished degree-one vertices modulo graph Reidemeister
moves applied away from the distinguished vertices. Generalizing previously
known results, we give topological interpretations of graphoids. There are
several applications to virtual graphoid theory. First, virtual graphoids are
suitable objects for studying knotted graphs with open ends arising in
proteins. Second, a virtual graphoid can be thought of as a way to represent a
virtual spatial graph without using as many crossings, which can be
advantageous for computing invariants
Invariants of multi-linkoids
In this paper, we extend the definition of a knotoid that was introduced by
Turaev, to multi-linkoids that consist of a number of knot and knotoid
components. We study invariants of multi-linkoids that lie in a closed
orientable surface, namely the Kauffman bracket polynomial, ordered bracket
polynomial, the Kauffman skein module, and the -invariant in relation with
generalized -graphs.Comment: 15 page
Knotoids, Braidoids and Applications
This paper is an introduction to the theory of braidoids. Braidoids are geometric objects analogous to classical braids, forming a counterpart theory to the theory of knotoids. We introduce these objects and their topological equivalences, and we conclude with a potential application to the study of proteins