TL;DR
This paper introduces universal oriented parity functors for free knots and knots on surfaces, providing a new algebraic framework for analyzing knot diagrams through parity assignments.
Contribution
It develops the concept of universal oriented parity functors, extending parity theory to free knots and surface knots with a unified algebraic approach.
Findings
Defines universal oriented parity functors for free knots.
Extends parity concepts to knots on surfaces.
Provides algebraic tools for knot diagram analysis.
Abstract
A parity is a rule to assign labels to the crossings of knot diagrams in a way compatible with Reidemeister moves. Parity functors can be viewed as parities which provide to each knot diagram its own coefficient group that contains parities of the crossings. In the article we describe the universal oriented parity functors for free knots and for knots in a fixed surface.
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Taxonomy
TopicsGeometric and Algebraic Topology