Diagram genus, generators and applications. (2018)

• Record Type: Book
• Further Information: Note: Alexander Stoimenow.
• Authors: Stoimenow, Alexander
• Contents: 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
• Publisher Details: Place of publication not identified : Chapman and Hall/CRC
• Publication Date: 2018
• Extent: 1 online resource (174 pages), (17 illustrations)
• Subjects: 514.2242; Knot theory
• Languages: English
• ISBNs: 9781315359984; 1315359987
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.