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QUANDLES AT FINITE TEMPERATURES I

PEDRO LOPES

Departamento de Matemática and Centro de Matemática Aplicada, Instituto Superior Técnico, Av. Rovisco Pais, 1049-001 Lisboa, Portugal

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https://doi.org/10.1142/S0218216503002378Cited by:13 (Source: Crossref)

Abstract

In [3] quandle cohomology is used to produce invariants for particular embeddings of codimension two; 2-cocycles give rise 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 the 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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