Homology and Cohomology of Topological Quandles
Georgy C. Luke, B. Subhash
TL;DR
This paper develops a homology and cohomology theory for topological quandles, linking it to existing quandle (co)homology, and uses cocycles to compute knot invariants.
Contribution
It introduces a new homology and cohomology framework for topological quandles and explores their relation to classical quandle (co)homology.
Findings
Established a relation between topological and classical quandle (co)homology
Used 1-topological quandle cocycles to compute knot invariants
Provided a method to derive state sum invariants from topological quandles
Abstract
A homology and cohomology theory for topological quandles are introduced. The relation between these (co)homology groups and quandle (co)homology groups are studied. The 1 - topological quandle cocycles are used to compute state sum invariants corresponding to knot diagrams.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Topological and Geometric Data Analysis