Generalizations of Quandle Cocycle Invariants and Alexander Modules from Quandle Modules

2004/01/15 by J. Scott Carter, Carter, J. Scott, Masahico Saito +1
Mathematics · #55N22 #55N99 #57M25 #57Q45 #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.GT #math.QA #msc:55N22 #msc:55N99 #msc:57M25 #msc:57Q45

paper · pdf · doi:10.48550/arxiv.math/0401183

Survey article submitted to the Conference ``Intellegence of Low Dimensional Topology,'' Shodo Shima, Japan 2003

arxiv created 2004/01/15 · openalex publication_date 2004/01/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a brief overview of some of our recent results in collaboration with other authors. The cocycle invariants of classical knots and knotted surfaces are summarized, and some applications are presented.

Citations

• A classifying invariant of knots, the knot quandle

Related

• Cocycle Knot Invariants, Quandle Extensions, and Alexander Matrices
• Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology
• Polynomial cocycles of Alexander quandles and applications
• Quandle Homology Theory and Cocycle Knot Invariants
• Quandle homotopy invariants of knotted surfaces