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Meta-Monoids, Meta-Bicrossed Products, and the Alexander Polynomial

2013/02/22 by Dror Bar-Natan, Bar-Natan, Dror, Sam Alexandre Selmani +2
Computer Science · Mathematics · #57M25 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.GT #math.QA #msc:57M25 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1302.5689

14 pages; minor changes; to appear in JKTR

openalex publication_date 2013/02/22 · arxiv created 2013/09/13 · arxiv updated 2013/09/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce a new invariant of tangles along with an algebraic framework in which to understand it. We claim that the invariant contains the classical Alexander polynomial of knots and its multivariable extension to links. We argue that of the computationally efficient members of the family of Alexander invariants, it is the most meaningful. These are lecture notes for talks given by the first author, written and completed by the second. The talks, with handouts and videos, are available at http://www.math.toronto.edu/drorbn/Talks/Regina-1206/. See also further comments at http://www.math.toronto.edu/drorbn/Talks/Caen-1206/#June8.

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