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Quandles at Finite Temperatures I

Pedro Lopes
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Abstract

In CJKLS quandle cohomology is used to produce invariants for particular embeddings of codimension two; 2-cocycles give to invariants for (classical) knots and 3-cocycles give rise to invariants for knotted surfaces. This is done by way of a notion of coloring of a diagram. Also, these invariants have the form of state-sums (or partition functions) used in Statistical Mechanics. By a careful analysis of these colorings of diagrams we are able to come up with new invariants which correspond to calculation of the partition function at finite temperatures.

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Pedro Lopes. 2001-05-12. Quandles at Finite Temperatures I. https://arxiv.org/abs/math/0105099

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