Computations of Quandle Cocycle Invariants of Knotted Curves and Surfaces

✍ Scribed by J.Scott Carter; Daniel Jelsovsky; Seiichi Kamada; Masahico Saito

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 597 KB
• Volume: 157
• Category: Article
• ISSN: 0001-8708
• DOI: 10.1006/aima.2000.1939

✦ Synopsis

State-sum invariants for knotted curves and surfaces using quandle cohomology were introduced by Laurel Langford and the authors (Quandle cohomology and state-sum invariants of knotted curves and surfaces, preprint). In this paper we present methods to compute the invariants and sample computations. Computer calculations of cohomological dimensions for some quandles are presented. For classical knots, Burau representations together with Maple programs are used to evaluate the invariants for knot table. For knotted surfaces in 4-space, movie methods and surface braid theory are used. Relations between the invariants and symmetries of knots are discussed.