2012/09/07 by Józef H. Przytycki, Jozef H. Przytycki, Przytycki, Jozef H. · 1 citation
Computer Science · Mathematics · #57M25 #Advanced Algebra and Logic #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M25
paper · pdf · doi:10.48550/arxiv.1209.1592
109 pages, 82 figures, Chapter III of the book "KNOTS: From combinatorics of knot diagrams to combinatorial topology based on knots"
arxiv created 2012/09/07 · openalex publication_date 2012/09/07 · arxiv updated 2012/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this chapter (Chapter III) we introduce the concept of Conway algebras (the notion related to entropic magmas) and describe invariants of links yielded by (partial) Conway algebras (including the Homflypt polynomial and signatures). We present, in detail, a proof (following the original Przytycki-Traczyk 1984 proof) of the existence of Conway type invariants. Then we describe Kauffman's method of constructing link invariants, in particular, giving the Kauffman polynomial of two variables. We develop a formalism, Kauffman algebras, analogous to that of Conway algebras. This chapter, along with chapters II, IV, and V of the book (already on arXiv), form the core of the first part of the book.