Desatando nudos y teoremas : grupo fundamental y teorema de Seifert Van Kampen
| dc.contributor.advisor | Giraldo Hernández, Carlos Andrés | |
| dc.contributor.author | Arciniegas Barreto, Yoseth Stiven | |
| dc.date.accessioned | 2025-03-11T15:11:35Z | |
| dc.date.available | 2025-03-11T15:11:35Z | |
| dc.date.created | 2024-11-14 | |
| dc.description | En el siguiente trabajo se realiza un estudio detallado sobre la construcción del grupo fundamental, comenzando con la definición de homotopía y las implicaciones de llevar este concepto a un contexto algebraico. Posteriormente, se aborda la construcción de grupos libres y grupos libres amalgamados, con el objetivo de presentar el teorema de Seifert Van Kampen y explorar una de sus aplicaciones en la teoría de nudos. A partir de este teorema se demuestra que el grupo del nudo puede considerarse en R^3 y S^3, ya que ambos son isomorfos. | |
| dc.description.abstract | This work presents a detailed study of the construction of the fundamental group, starting with the definition of homotopy and the implications of bringing this concept into an algebraic context. Subsequently, the construction of free groups and amalgamated free products is addressed, with the aim of presenting the Seifert–van Kampen theorem and exploring one of its applications in knot theory. Using this theorem, it is shown that the knot group can be considered in R^3 or S^3, as both are isomorphic. | |
| dc.format.mimetype | ||
| dc.identifier.uri | http://hdl.handle.net/11349/93491 | |
| dc.language.iso | spa | |
| dc.publisher | Universidad Distrital Francisco José de Caldas | |
| dc.relation.references | Colin C. Adams. The knot book. American Mathematical Society, Providence, RI, 2004. An elementary introduction to the mathematical theory of knots, Revised reprint of the 1994 original. | |
| dc.relation.references | Allen Hatcher. Algebraic topology. Cambridge University Press, Cambridge, 2002. | |
| dc.relation.references | Thomas W. Hungerford. Algebra. Holt, Rinehart and Winston, Inc., New York-Montreal, Que.- London, 1974. | |
| dc.relation.references | John M. Lee. Introduction to topological manifolds, volume 202 of Graduate Texts in Mathematics. Springer, New York, second edition, 2011. | |
| dc.relation.references | Elon Lages Lima. Fundamental groups and covering spaces. A K Peters, Ltd., Natick, MA, 2003. Translated from the Portuguese by Jonas Gomes. | |
| dc.relation.references | James R. Munkres. Topology. Prentice Hall, Inc., Upper Saddle River, NJ, second edition, 2000. | |
| dc.relation.references | Dale Rolfsen. Knots and links, volume No. 7 of Mathematics Lecture Series. Publish or Perish Inc. Berkeley ,CA, 1976. | |
| dc.relation.references | Gustavo Rubiano. Fundamentos de topología alebgraica, 1a. edicion. Universidad Nacional de Colombia, sede Bogota, 2007. | |
| dc.rights.acceso | Abierto (Texto Completo) | |
| dc.rights.accessrights | OpenAccess | |
| dc.subject | Homotopía | |
| dc.subject | Grupo fundamental | |
| dc.subject | Grupo libre | |
| dc.subject | Espacio conexo | |
| dc.subject | Nudo | |
| dc.subject | Grupo del nudo | |
| dc.subject.keyword | Homotopy | |
| dc.subject.keyword | Fundamental group | |
| dc.subject.keyword | Free group | |
| dc.subject.keyword | Connected space | |
| dc.subject.keyword | Knot | |
| dc.subject.keyword | Knot group | |
| dc.subject.lemb | Matemáticas -- Tesis y disertaciones académicas | |
| dc.subject.lemb | Teoría de nudos | spa |
| dc.subject.lemb | Teorema de Seifert-van Kampen | spa |
| dc.subject.lemb | Matemáticas topológicas | spa |
| dc.subject.lemb | Topología algebraica | spa |
| dc.subject.lemb | Estructuras algebraicas | spa |
| dc.title | Desatando nudos y teoremas : grupo fundamental y teorema de Seifert Van Kampen | |
| dc.title.titleenglish | Untangling knots and theorems: fundamental group and the Seifert Van Kampen theorem | |
| dc.type | bachelorThesis | |
| dc.type.coar | http://purl.org/coar/resource_type/c_7a1f | |
| dc.type.degree | Monografía | |
| dc.type.driver | info:eu-repo/semantics/bachelorThesis |
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