On the two-parabolic subgroups of sl(2,c)
We consider homomorphisms $H_{t}$ from the free group $F$ of rank $2$ onto the subgroup of SL$(2,\mathbb{C})$ that is generated by two parabolic matrices. Up to conjugation, $H_{t}$ depends only on one complex parameter $t$. We study the possible relators, that is, the words $w\in F$ with $w\neq 1$...
- Autores:
-
Pommerenke, Christian
Toro, Margarita
- Tipo de recurso:
- Article of journal
- Fecha de publicación:
- 2011
- Institución:
- Universidad Nacional de Colombia
- Repositorio:
- Universidad Nacional de Colombia
- Idioma:
- spa
- OAI Identifier:
- oai:repositorio.unal.edu.co:unal/39448
- Acceso en línea:
- https://repositorio.unal.edu.co/handle/unal/39448
http://bdigital.unal.edu.co/29545/
- Palabra clave:
- Representation
Parabolic
Wirtinger presentation
Two-generated groups
Homomorphism
Longitude
15A30
57M05
- Rights
- openAccess
- License
- Atribución-NoComercial 4.0 Internacional
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Atribución-NoComercial 4.0 InternacionalDerechos reservados - Universidad Nacional de Colombiahttp://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccesshttp://purl.org/coar/access_right/c_abf2Pommerenke, Christian4999ea34-cb26-4530-bec3-81efd88b32c5300Toro, Margarita41238712-8669-499d-bf35-cf4a7ab2dc503002019-06-28T03:53:37Z2019-06-28T03:53:37Z2011https://repositorio.unal.edu.co/handle/unal/39448http://bdigital.unal.edu.co/29545/We consider homomorphisms $H_{t}$ from the free group $F$ of rank $2$ onto the subgroup of SL$(2,\mathbb{C})$ that is generated by two parabolic matrices. Up to conjugation, $H_{t}$ depends only on one complex parameter $t$. We study the possible relators, that is, the words $w\in F$ with $w\neq 1$ such that $H_{t}(w)=I$ for some $t\in\mathbb{C}$. We find several families of relators. 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.application/pdfspaUniversidad Nacuional de Colombia; Sociedad Colombiana de matemáticashttp://revistas.unal.edu.co/index.php/recolma/article/view/28062Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de MatemáticasRevista Colombiana de MatemáticasRevista Colombiana de Matemáticas; Vol. 45, núm. 1 (2011); 37-50 0034-7426Pommerenke, Christian and Toro, Margarita (2011) On the two-parabolic subgroups of sl(2,c). Revista Colombiana de Matemáticas; Vol. 45, núm. 1 (2011); 37-50 0034-7426 .On the two-parabolic subgroups of sl(2,c)Artículo de revistainfo:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1http://purl.org/coar/version/c_970fb48d4fbd8a85Texthttp://purl.org/redcol/resource_type/ARTRepresentationParabolicWirtinger presentationTwo-generated groupsHomomorphismLongitude15A3057M05ORIGINAL28062-142412-1-PB.htmltext/html6630https://repositorio.unal.edu.co/bitstream/unal/39448/1/28062-142412-1-PB.htmlf8cd19ba41d101ae78ec5ea66f1bc67fMD5128062-99516-1-PB.pdfapplication/pdf444280https://repositorio.unal.edu.co/bitstream/unal/39448/2/28062-99516-1-PB.pdf62281a87fd6dbdd1c9bff8883b221584MD52THUMBNAIL28062-99516-1-PB.pdf.jpg28062-99516-1-PB.pdf.jpgGenerated Thumbnailimage/jpeg4840https://repositorio.unal.edu.co/bitstream/unal/39448/3/28062-99516-1-PB.pdf.jpg5c5be5c7cc7b815d1937c1bab52baba8MD53unal/39448oai:repositorio.unal.edu.co:unal/394482024-01-20 23:06:26.893Repositorio Institucional Universidad Nacional de Colombiarepositorio_nal@unal.edu.co |
| dc.title.spa.fl_str_mv |
On the two-parabolic subgroups of sl(2,c) |
| title |
On the two-parabolic subgroups of sl(2,c) |
| spellingShingle |
On the two-parabolic subgroups of sl(2,c) Representation Parabolic Wirtinger presentation Two-generated groups Homomorphism Longitude 15A30 57M05 |
| title_short |
On the two-parabolic subgroups of sl(2,c) |
| title_full |
On the two-parabolic subgroups of sl(2,c) |
| title_fullStr |
On the two-parabolic subgroups of sl(2,c) |
| title_full_unstemmed |
On the two-parabolic subgroups of sl(2,c) |
| title_sort |
On the two-parabolic subgroups of sl(2,c) |
| dc.creator.fl_str_mv |
Pommerenke, Christian Toro, Margarita |
| dc.contributor.author.spa.fl_str_mv |
Pommerenke, Christian Toro, Margarita |
| dc.subject.proposal.spa.fl_str_mv |
Representation Parabolic Wirtinger presentation Two-generated groups Homomorphism Longitude 15A30 57M05 |
| topic |
Representation Parabolic Wirtinger presentation Two-generated groups Homomorphism Longitude 15A30 57M05 |
| description |
We consider homomorphisms $H_{t}$ from the free group $F$ of rank $2$ onto the subgroup of SL$(2,\mathbb{C})$ that is generated by two parabolic matrices. Up to conjugation, $H_{t}$ depends only on one complex parameter $t$. We study the possible relators, that is, the words $w\in F$ with $w\neq 1$ such that $H_{t}(w)=I$ for some $t\in\mathbb{C}$. We find several families of relators. 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. |
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2011 |
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2011 |
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2019-06-28T03:53:37Z |
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2019-06-28T03:53:37Z |
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Artículo de revista |
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http://purl.org/coar/resource_type/c_2df8fbb1 |
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info:eu-repo/semantics/article |
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https://repositorio.unal.edu.co/handle/unal/39448 |
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http://bdigital.unal.edu.co/29545/ |
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spa |
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spa |
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http://revistas.unal.edu.co/index.php/recolma/article/view/28062 |
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Universidad Nacional de Colombia Revistas electrónicas UN Revista Colombiana de Matemáticas Revista Colombiana de Matemáticas |
| dc.relation.ispartofseries.none.fl_str_mv |
Revista Colombiana de Matemáticas; Vol. 45, núm. 1 (2011); 37-50 0034-7426 |
| dc.relation.references.spa.fl_str_mv |
Pommerenke, Christian and Toro, Margarita (2011) On the two-parabolic subgroups of sl(2,c). Revista Colombiana de Matemáticas; Vol. 45, núm. 1 (2011); 37-50 0034-7426 . |
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Derechos reservados - Universidad Nacional de Colombia |
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Atribución-NoComercial 4.0 Internacional |
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info:eu-repo/semantics/openAccess |
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Atribución-NoComercial 4.0 Internacional Derechos reservados - Universidad Nacional de Colombia http://creativecommons.org/licenses/by-nc/4.0/ http://purl.org/coar/access_right/c_abf2 |
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