On the two-parabolic subgroups of SL (2; C)
We consider homomorphisms Ht from the free group F of rank 2 onto the subgroup of SL(2;C) that is generated by two parabolic matrices. Up to conjugation, Ht depends only on one complex parameter t. We study the possible relators, that is, the words w 2 F with w 6= 1 such that Ht(w) = I for some t 2...
- Autores:
- Tipo de recurso:
- Fecha de publicación:
- 2011
- Institución:
- Ministerio de Ciencia, Tecnología e Innovación
- Repositorio:
- Repositorio Minciencias
- Idioma:
- eng
- OAI Identifier:
- oai:repositorio.minciencias.gov.co:20.500.14143/22009
- Acceso en línea:
- https://repositorio.minciencias.gov.co/handle/20.500.14143/22009
- Palabra clave:
- Teoría de los números
Teoría de anillos
Teoría de grupos
Topología algebraica
Variables reales
Homomorfismos
Relaciones (matemáticas)
- Rights
- License
- http://purl.org/coar/access_right/c_f1cf
| Summary: | We consider homomorphisms Ht from the free group F of rank 2 onto the subgroup of SL(2;C) that is generated by two parabolic matrices. Up to conjugation, Ht depends only on one complex parameter t. We study the possible relators, that is, the words w 2 F with w 6= 1 such that Ht(w) = I for some t 2 C. We and several families of realtors. Of particular interest here are relators connected with 2-bridge knots, which we consider in a purely algebraic setting. We describe an algorithm to determine whether a given word is a possible relator. Key words and phrases. Representation, Parabolic, Wirtinger presentation, Two- generated groups, Homomorphism, Longitude. |
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