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In 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. The 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.
This volume represents the final definitive report on the archaeological work carried out at Spynie Palace between 1986 and 1994.
This overview of the religious customs of ancient cultures boasts an international selection of contributors, all of whom are leading scholars in their field. The cultural practices of popular as well as formal religion are explored in detail, giving an impression of all, not only elite societies. Every topic is placed in its own cultural context, while bearing in mind its relevance to a wider historical and sociological debate. The result is an erudite and thoroughly readable handbook to ancient religions, from Palaeolithic cave art to the rituals of Aztec and Inca civilizations.