On Skein Algebras And Sl_2(C)-Character Varieties
| dc.creator | Przytycki, Jozef H. | |
| dc.creator | Sikora, Adam S. | |
| dc.date | 1997-05-15 | |
| dc.date | 1998-05-31 | |
| dc.date.accessioned | 2026-07-07T09:08:47Z | |
| dc.date.available | 2026-07-07T09:08:47Z | |
| dc.description | This paper gives insight into intriguing connections between two apparently unrelated theories: the theory of skein modules of 3-manifolds and the theory of representations of groups into special linear groups of 2 by 2 matrices. Let R be a ring with an invertible element A. For any 3-manifold M one can assign an R-module called the Kauffman bracket skein module of M. If A^2=1 then this module has a structure of an R-algebra. We investigate this structure and, in particular, we prove that if R is the field of complex numbers then this algebra is isomorphic to the (unreduced) coordinate ring of the SL_2-character variety of pi_1(M). Using that result we develop a theory of Sl_2-character varieties by use of topological methods. We also assign to any surface a relative Kauffman bracket skein algebra. We prove several results about this non-commutative algebra. Our work should be considered in the context of the book of Brumfiel and Hilden `SL(2) Representations of Finitely Presented Groups,' Cont. Math 187. In particular we give a topological interpretation to algebraic objects considered in that book. | |
| dc.description | 47 pages, Latex, 34 figures, to appear in Topology | |
| dc.identifier | https://arxiv.org/abs/q-alg/9705011 | |
| dc.identifier | http://arxiv.org/abs/q-alg/9705011 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/150845 | |
| dc.subject | Quantum Algebra | |
| dc.title | On Skein Algebras And Sl_2(C)-Character Varieties | |
| dc.type | text |