Titlebook: Lectures in Knot Theory; An Exploration of Co Józef H. Przytycki,Rhea Palak Bakshi,Deborah Weeks Textbook 2024 The Editor(s) (if applicable

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978-3-031-40043-8The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Lectures in Knot Theory978-3-031-40044-5Series ISSN 0172-5939 Series E-ISSN 2191-6675

無政府主義者

https://doi.org/10.1007/978-3-031-40044-5Knots and links; Fox colorings; Gram determinants; History of knots; Jones polynomial; Khovanov homology;

尖酸一點

圖畫文字

Goeritz and Seifert Matrices,the checkerboard coloring of a link diagram and the second using an oriented surface bounded by a link. We discuss several link invariants coming from the matrix including the determinant, the signature, the Alexander-Conway polynomial, and the Tristram-Levine signature.

staging

The Jones Polynomial and Kauffman Bracket Polynomial,s lecture, we describe basic properties of these polynomials including mysterious relations with Fox 3??coloring. We also discuss Montesinos-Nakanishi 3??move conjecture and its solution using the Burnside group of link. We end by discussing the Nakanishi 4-move conjecture, from 1979.

精密

The Temperley-Lieb Algebra and the Artin Braid Group,not theory and 3-manifold invariants. For example, its connection to knot theory stems from Louis H. Kauffman’s interpretation of the Temperley-Lieb algebra as a diagrammatic algebra consisting of .-tangles as its basis. In this lecture we explore the basics of the Temperley-Lieb algebra and Artin braid group.

receptors

The Kauffman Bracket Skein Module and Algebra of Surface I-Bundles,ter varieties, cluster algebras, and quantum Teichmüller spaces. In this lecture we explore some of these connections and discuss the structure of the Kauffman bracket skein algebras of several thickened surfaces.