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Diagram Genus, Generators, and Applications (Hardcover) (Alexander Stoimenow)
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This book on knot theory is primarily concerned with the genus of knot diagrams or the maximal number of crossings of generators which allows the reader to complete their classification for knots of genus four. People have studied these ideas for many years as the applications found can lead to the treatment of cannonical surfaces from a combintorial point of view. In this book an algortihmic approach is used to improve what we know about knots. This has lead the author to develope an alternative approach which is based on the special diagram algorithm discovered by Hirasawa. This approach allows us to improve on what we know about the knot case and extend it to links.