Traces on the skein algebra of the torus
| dc.creator | McLendon, Michael | |
| dc.date | 2006-03-14 | |
| dc.date.accessioned | 2026-07-07T07:06:53Z | |
| dc.date.available | 2026-07-07T07:06:53Z | |
| dc.description | For 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.description | 8 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0603343 | |
| dc.identifier | http://arxiv.org/abs/math/0603343 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/110188 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57M27 | |
| dc.title | Traces on the skein algebra of the torus | |
| dc.type | text |