Three-page approach to knot theory. Encoding and local moves
- 78 Downloads
In the present paper, we suggest a new combinatorial approach to knot theory based on embeddings of knots and links into a union of three half-planes with the same boundary. The idea to embed knots into a “book” is quite natural and was considered already in . Among recent papers on embeddings of knots into a book with infinitely many pages, we mention  and  (see also references therein).
The restriction of the number of pages to three (or any other number ≥3) provides a convenient way toencode links by words in a finite alphabet. For those words, we give a finite set of local changes that realizes the equivalence of links by analogy with the Reidemeister moves for planar link diagrams.
KeywordsSimple Move Polygonal Line Elementary Move Isotopy Class Reidemeister Move
Unable to display preview. Download preview PDF.