TL;DR
This paper provides a simplified skein characterization of Conway's potential function for colored links, avoiding complex axioms and computer algebra, and offers insights into the Alexander-Conway polynomial of knots.
Contribution
It introduces a new, simpler skein characterization of the Conway potential function that does not rely on crossing smoothing or computer algebra tools.
Findings
Simplified skein characterization of CPF
Reduction scheme in twisted group-algebra used in proof
Characterization of Alexander-Conway polynomial for knots
Abstract
The Conway potential function (CPF) for colored links is a convenient version of the multi-variable Alexander-Conway polynomial. We give a skein characterization of CPF, much simpler than the one by Murakami. In particular, Conway's `smoothing of crossings' is not in the axioms. The proof uses a reduction scheme in a twisted group-algebra , where is a braid group and is a domain of multi-variable rational fractions. The proof does not use computer algebra tools. An interesting by-product is a characterization of the Alexander-Conway polynomial of knots.
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