Homology Groups of Symmetric Quandles and Cocycle Invariants of Links and Surface-links
Seiichi Kamada, Kanako Oshiro
TL;DR
This paper introduces a new class of quandles with good involutions and their homology groups, enabling the definition of cocycle invariants for non-oriented and non-orientable links and surface-links, aiding in topological estimations.
Contribution
It extends quandle cocycle invariants to non-oriented and non-orientable links using good involutions, providing new tools for topological analysis.
Findings
Defined homology groups for quandles with good involutions
Established cocycle invariants for non-orientable links and surface-links
Applied invariants to estimate minimal triple point numbers
Abstract
We introduce the notion of a quandle with a good involution and its homology groups. Carter et al. defined quandle cocycle invariants for oriented links and oriented surface-links. By use of good involutions, quandle cocyle invariants can be defined for links and surface-links which are not necessarily oriented or orientable. The invariants can be used in order to estimate the minimal triple point numbers of non-orientable surface-links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research