Rack module enhancements of counting invariants
Aaron Haas, Garret Heckel, Sam Nelson, Jonah Yuen, and Qingcheng Zhang
Source: Osaka J. Math. Volume 49, Number 2
(2012), 471-488.
Abstract
We introduce a modified rack algebra $\mathbb{Z}[X]$ for racks
$X$ with finite rack rank $N$. We use representations of $\mathbb{Z}[X]$
into rings, known as rack modules, to define enhancements
of the rack counting invariant for classical and virtual knots
and links. We provide computations and examples to show that
the new invariants are strictly stronger than the unenhanced
counting invariant and are not determined by the Jones or
Alexander polynomials.
Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.ojm/1340197935
Zentralblatt MATH identifier: 06060695
Mathematical Reviews number (MathSciNet): MR2945758
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