Diagram Genus, Generators, and Applications /

Bibliographic Details
Main Author:	Stoimenow, Alexander (Author)
Corporate Author:	Taylor & Francis
Format:	eBook
Language:	English
Published:	Boca Raton, FL : Chapman and Hall/CRC, [2018]
Edition:	First edition.
Series:	Chapman & Hall/CRC Monographs and Research Notes in Mathematics.
Subjects:	Knot theory. Knot polynomials. Mathematics > Topology. Théorie des nœuds. Polynômes des nœuds. MATHEMATICS > Combinatorics. MATHEMATICS > Arithmetic. Bennequin surface. braid index of alternating knots. canonical Seifert surfaces. combinatorial knot theory. Knot diagrams. polynomial invariant. surfaces of genus 4. Knot polynomials Knot theory Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of 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 diagramsCrossing number and writhe Knotation and not-tables Seifert surfaces and genera Graphs Diagrammatic movesBraids and braid representations Link polynomials MWF inequality, Seifert graph, and graph index The signature Genus generatorsKnots 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 Hostes 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.