Irreducible components in an algebraic variety of representations of a family of one-relator groups
| dc.creator | Liriano, S. | |
| dc.date | 2006-10-01 | |
| dc.date | 2006-10-03 | |
| dc.date.accessioned | 2026-07-07T07:28:34Z | |
| dc.date.available | 2026-07-07T07:28:34Z | |
| dc.description | Given a finitely generated group G, the set Hom(G,SL_2 C) inherits the structure of an algebraic variety R(G)called the "representation variety" of G. This algebraic variety is an invariant of G. Let G_{pt}=< a, b; a^p= b^t>, where p, t are integers greater than one. In this paper a formula is produced yielding the number of four dimensional irreducible components of the affine algebraic variety R(G_{pt}). A direct consequence of the main theorem of this paper is that if K is a torus knot, then its genus equals the number of four dimensional components of R(G_{pt}) corresponding to its knot group G_{pt}. | |
| dc.description | 5 pages | |
| dc.identifier | https://arxiv.org/abs/math/0610039 | |
| dc.identifier | http://arxiv.org/abs/math/0610039 | |
| dc.identifier | Internat. J. Algebra Comput. 9 (1999), 129-133 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/117778 | |
| dc.subject | Group Theory | |
| dc.subject | 20F38, 14Q99 | |
| dc.title | Irreducible components in an algebraic variety of representations of a family of one-relator groups | |
| dc.type | text |