On Upper Bounds for Toroidal Mosaic Numbers
Geometric Topology
2014-04-16 v2 Quantum Physics
Abstract
In this paper, we work to construct mosaic representations of knots on the torus, rather than in the plane. This consists of a particular choice of the ambient group, as well as different definitions of contiguous and suitably connected. We present conditions under which mosaic numbers might decrease by this projection, and present a tool to measure this reduction. We show that the order of edge identification in construction of the torus sometimes yields different resultant knots from a given mosaic when reversed. Additionally, in the Appendix we give the catalog of all 2 by 2 torus mosaics.
Keywords
Cite
@article{arxiv.1206.4227,
title = {On Upper Bounds for Toroidal Mosaic Numbers},
author = {Michael J. Carlisle and Michael S. Laufer},
journal= {arXiv preprint arXiv:1206.4227},
year = {2014}
}
Comments
10 pages, 111 figures