Grid Movies

2013/03/07 by M. J. Graham, Graham, Matthew
Computer Science · #Artificial Intelligence in Games #Data Visualization and Analytics #Distributed and Parallel Computing Systems #FOS: Mathematics #Geometric Topology (math.GT)

paper · pdf · doi:10.48550/arxiv.1303.1831

openalex publication_date 2013/03/07 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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.

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