{"product_id":"diagram-genus-generators-applications","title":"Diagram Genus Generators \u0026 Applications","description":"\u003cp\u003eIn knot theory, diagrams of a given canonical genus can be described by means of a finite number of patterns (\"generators\"). \u003cstrong\u003eDiagram Genus, Generators and Applications\u003c\/strong\u003e 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.\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThe 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 Hirasawa’s 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 the genus 4 classification, including the braid index, polynomial invariants, hyperbolic volume, and Vassiliev invariants. The final chapter presents further research related to generators, which helps readers see applications of generators in a broader context.\u003c\/p\u003e","brand":"MediaPlace","offers":[{"title":"Default Title","offer_id":57311068389758,"sku":"NW9781498733809","price":143.98,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1379\/1261\/files\/9781498733809.jpg?v=1778583779","url":"https:\/\/mediaplace.com\/products\/diagram-genus-generators-applications","provider":"MediaPlace","version":"1.0","type":"link"}