Grid Movies
Geometric Topology
2014-07-21 v2
Abstract
We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that grid planar isotopy classes are in 1-1 correspondence with smooth planar isotopy classes by using a new planar grid algorithm that takes a smooth knot diagram to a grid diagram. We then present generalizations of both the smooth and grid movie theorems that apply to surfaces with boundary.
Cite
@article{arxiv.1303.1831,
title = {Grid Movies},
author = {Matthew Graham},
journal= {arXiv preprint arXiv:1303.1831},
year = {2014}
}
Comments
Original comments: 38 pages, 19 figures Revision comments: Enlarged movie moves and made a number of minor corrections throughout