Diagram Genus, Generators, and Applications

ISBN: 9781498733809 出版年：2018 页码：192 Stoimenow, Alexander CRC Press

Introduction The beginning of knot theory Reidemeister moves and invariants Combinatorial knot theory Genera of knots Overview of results Issues of presentation Further applications Preliminaries Knots and diagrams Crossing number and writhe Knotation and not-tables Seifert surfaces and genera Graphs Diagrammatic moves Braids and braid representations Link polynomials MWF inequality, Seifert graph, and graph index The signature Genus generators Knots vs. links The maximal number of generator crossings and ~-equivalence classes Generator crossing number inequalities An algorithm for special diagrams Proof of the inequalities Applications and improvements Generators of genus 4 Unknot diagrams, non-trivial polynomials, and achiral knots Some preparations and special cases Reduction of unknot diagrams Simplifications Examples Non-triviality of skein and Jones polynomial On the number of unknotting Reidemeister moves Achiral knot classification The signature Braid index of alternating knots Motivation and history Hidden Seifert circle problem Modifying the index Simplified regularization A conjecture Minimal string Bennequin surfaces Statement of result The restricted index Finding a minimal string Bennequin surface The Alexander polynomial of alternating knots Hoste's conjecture The log-concavity conjecture Complete linear relations by degree Outlook Legendrian invariants and braid index Minimal genus and fibering of canonical surfaces Wicks forms, markings, and enumeration of alternating knots by genus Crossing numbers Canonical genus bounds hyperbolic volume The relation between volume and the slN polynomial Everywhere equivalent links