Digital knots

摘要

We define digital (6-)knots in Z3, and discuss how they are related to isothetic polygonal knots in R3. We introduce a class of topology-preserving “simple deformations” (SD) of digital images, and show that isomorphic knots have digitizations that differ by SD, and conversely. We also define “regular position” for isothetic links and digital links, and show that SD can be used to put any digital knot into such a position and to perform “Reidemeister moves” on the resulting projection.