Traces on the skein algebra of the torus

dc.creatorMcLendon, Michael
dc.date2006-03-14
dc.date.accessioned2026-07-07T07:06:53Z
dc.date.available2026-07-07T07:06:53Z
dc.descriptionFor a surface $F$, the Kauffman bracket skein module of $F \times [0,1]$, denoted $K(F)$, admits a natural multiplication which makes it an algebra. When specialized at a complex number $t$, nonzero and not a root of unity, we have $K_t(F)$, a vector space over $\mathbb{C}$. In this paper, we will use the product-to-sum formula of Frohman and Gelca to show that the vector space $K_t(T^2)$ has five distinct traces. One trace, the Yang-Mills measure, is obtained by picking off the coefficient of the empty skein. The other four traces on $K_t(T^2)$ correspond to each of the four $\mathbb{Z}_2$ homology classes of the torus.
dc.description8 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0603343
dc.identifierhttp://arxiv.org/abs/math/0603343
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110188
dc.subjectGeometric Topology
dc.subject57M27
dc.titleTraces on the skein algebra of the torus
dc.typetext

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