Elementary proof of existence of the Alexander-Conway polynomial
T. Garaev
TL;DR
This paper provides a clear and detailed proof of the existence of the Alexander-Conway polynomial for links in 3-dimensional space, clarifying foundational aspects of knot theory.
Contribution
It offers an elementary and detailed proof of the Alexander-Conway polynomial's existence, simplifying previous complex proofs by other mathematicians.
Findings
Proof confirms the polynomial's existence for links in 3D space
Clarifies foundational aspects of knot invariants
Provides an accessible proof for educational purposes
Abstract
We present an accurate detailed exposition of the proof of existence of the Alexander-Conway polynomial (of links in 3-dimensional space). Other proofs were given by J. Alexander, J. Conway, V. Mantourov and L. Kauffman.
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Quantum chaos and dynamical systems