Generalizations of Knotoids and Spatial Graphs
Geometric Topology
2022-09-07 v1
Abstract
In 2010, Turaev introduced knotoids as a variation on knots that replaces the embedding of a circle with the embedding of a closed interval with two endpoints which here we call poles. We define generalized knotoids to allow arbitrarily many poles, intervals, and circles, each pole corresponding to any number of interval endpoints, including zero. This theory subsumes a variety of other related topological objects and introduces some particularly interesting new cases. We explore various analogs of knotoid invariants, including height, index polynomials, bracket polynomials and hyperbolicity. We further generalize to knotoidal graphs, which are a natural extension of spatial graphs that allow both poles and vertices.
Keywords
Cite
@article{arxiv.2209.01922,
title = {Generalizations of Knotoids and Spatial Graphs},
author = {Colin Adams and Alexandra Bonat and Maya Chande and Joye Chen and Maxwell Jiang and Zachary Romrell and Daniel Santiago and Benjamin Shapiro and Dora Woodruff},
journal= {arXiv preprint arXiv:2209.01922},
year = {2022}
}
Comments
43 pages, 22 figures