TL;DR
This paper characterizes the signature functions of knots, providing necessary and sufficient conditions for a function to be realized as a knot's signature function, which is an integer-valued step function on the unit circle.
Contribution
It offers a complete characterization of signature functions of knots, advancing understanding of knot invariants and their properties.
Findings
Provides necessary and sufficient conditions for a function to be a knot signature function
Characterizes the signature function as an integer-valued step function on the unit circle
Enhances the theoretical understanding of knot invariants
Abstract
The signature function of a knot is an integer-valued step function on the unit circle in the complex plane. Necessary and sufficient conditions for a function to be the signature function of a knot are presented.
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