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- DescriptionIn kt theory, diagrams of a given canical 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 canical genus: the genus of kt diagrams. The author explores recent research on the combinatorial theory of kts and supplies proofs for a number of theorems. The book begins with an introduction to the origin of kt 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 kt generators one genus further to complete their classification for genus 4. Subsequent chapters cover applications of the genus 4 classification, including the braid index, polymial 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.
- Author BiographyAlexander Stoimenow is an assistant professor in the GIST College at the Gwangju Institute of Science and Technology. He was previously an assistant professor in the Department of Mathematics at Keimyung University, Daegu, South Korea. His research covers several areas of knot theory, with relations to combinatorics, number theory, and algebra. He earned a PhD from the Free University of Berlin.
- Author(s)Alexander Stoimenow
- PublisherTaylor & Francis Inc
- Date of Publication04/03/2016
- SubjectScience & Mathematics: Textbooks & Study Guides
- Series TitleMonographs and Research Notes in Mathematics
- Place of PublicationPortland
- Country of PublicationUnited States
- ImprintProductivity Press
- Content Note17 black & white illustrations, 1 black & white tables
- Weight408 g
- Width156 mm
- Height235 mm
- Spine15 mm
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