Diagram Genus, Generators, and Applications

Taylor & Francis Inc

Diagram Genus, Generators, and ApplicationsAuthor(s): Alexander Stoimenow\nFormat: Hardback\nPublisher: Taylor & Francis Inc, United States\nImprint: Chapman & Hall/CRC\nISBN-13: 9781498733809, 978-1498733809\nSynopsis\nIn knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns (\""generators\""). Diagram Genus, Generators and Applications presents a self-contained account of the canonical genus: the genus of knot diagrams. The author explores recent research on the combinatorial theory of knots and supplies proofs for a number of theorems.\n\nThe book begins with an introduction to the origin of knot tables and the background details, including diagrams, surfaces, and invariants. It then derives a new description of generators using Hirasawas algorithm and extends this description to push the compilation of knot generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of .