Artículo
Grana, M.; Turaev, V. "Knot theory for self-indexed graphs" (2005) Transactions of the American Mathematical Society. 357(2):535-553
Este artículo es de Acceso Abierto y puede ser descargado en su versión final desde nuestro repositorio
Consulte la política de Acceso Abierto del editor
Abstract:
We introduce and study so-called self-indexed graphs. These are (oriented) finite graphs endowed with a map from the set of edges to the set of vertices. Such graphs naturally arise from classical knot and link diagrams. In fact, the graphs resulting from link diagrams have an additional structure, an integral flow. We call a self-indexed graph with integral flow a comte. The analogy with links allows us to define transformations of comtes generalizing the Reidemeister moves on link diagrams. We show that many invariants of links can be generalized to comtes, most notably the linking number, the Alexander polynomials, the link group, etc. We also discuss finite type invariants and quandle cocycle invariants of comtes.
Registro:
| Documento: | Artículo |
| Título: | Knot theory for self-indexed graphs |
| Autor: | Grana, M.; Turaev, V. |
| Filiación: | Departamento de Matemática, FCEYN, Ciudad Universitaria, PAB. I, 1428 Buenos Aires, Argentina IRMA, CNRS, Université Louis Pasteur, 7 Rue René Descartes, 67084 Strasbourg Cedex, France |
| Año: | 2005 |
| Volumen: | 357 |
| Número: | 2 |
| Página de inicio: | 535 |
| Página de fin: | 553 |
| DOI: | http://dx.doi.org/10.1090/S0002-9947-04-03625-6 |
| Título revista: | Transactions of the American Mathematical Society |
| Título revista abreviado: | Trans. Am. Math. Soc. |
| ISSN: | 00029947 |
| PDF: | https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00029947_v357_n2_p535_Grana.pdf |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029947_v357_n2_p535_Grana |
Referencias:
- Andruskiewitsch, N., Grana, M., From racks to pointed Hopf algebras (2003) Adv. Math., 178 (2), pp. 177-243. , [AG]
- Burde, G., Zieschang, H., Knots (1985) De Gruyter Studies in Mathematics, 5. , [BZ] Walter de Gruyter & Co., Berlin . MR 87b:57004
- Carter, J.S., Jelsovsky, D., Kamada, S., Langford, L., Saito, M., Quandle cohomology and state-sum invariants of knotted curves and surfaces (2003) Trans. Amer. Math. Soc., 355 (10), pp. 3947-3989. , [CJKLS] (electronic)
- Christensen, A., Rosebrock, S., On the impossibility of a generalization of the HOMFLY polynomial to LOGs (1996) Ann. Fac. Sci. Toulouse Math. (6), 5 (3), pp. 407-419. , [CR] . MR 97m:57003
- Etingof, P., Grana, M., On rack cohomology (2003) J. Pure Appl. Algebra, 177 (1), pp. 49-59. , [EG] . MR 2004e:55006
- Fenn, R., Rourke, C., Sanderson, B., An introduction to species and the rack space (1992) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., 309, pp. 33-55. , [FRS] Topics in knot theory (Erzurum), Kluwer Acad. Publ., Dordrecht . MR 95g:57022
- Gilbert, N.D., Howie, J., LOG groups and cyclically presented groups (1995) J. Algebra, 174 (1), pp. 118-131. , [GH] . MR 96g:20042
- Goussarov, M., Polyak, M., Viro, O., Finite-type invariants of classical and virtual knots (2000) Topology, 39 (5), pp. 1045-1068. , [GPV] . MR 2001i:57017
- Joyce, D., A classifying invariant of knots, the knot quandle (1982) J. Pure Appl. Alg., 23 (1), pp. 37-65. , [J] . MR 83m:57007
- Kauffman, L., Virtual knots theory (1999) European J. Combin., 20 (7), pp. 663-690. , [K] MR 2000i:57011
- Matveev, S., Distributive groupoids in knot theory (1982) Mat. Sb. (N.S.), 119 (161), pp. 78-88. , [Ma]
- (1984) Math. USSR-Sb., 47 (1), pp. 73-83. , English translation . MR 84e:57008
- Rolfsen, D., Knots and links (1990) Mathematics Lecture Series, 7. , [R] Corrected reprint of the 1976 original , Publish or Perish, Inc., Houston, TX . MR 95c:57018
Citas:
---------- APA ----------
Grana, M. & Turaev, V. (2005) . Knot theory for self-indexed graphs. Transactions of the American Mathematical Society, 357(2), 535-553.http://dx.doi.org/10.1090/S0002-9947-04-03625-6
---------- CHICAGO ----------
Grana, M., Turaev, V. "Knot theory for self-indexed graphs" . Transactions of the American Mathematical Society 357, no. 2 (2005) : 535-553.http://dx.doi.org/10.1090/S0002-9947-04-03625-6
---------- MLA ----------
Grana, M., Turaev, V. "Knot theory for self-indexed graphs" . Transactions of the American Mathematical Society, vol. 357, no. 2, 2005, pp. 535-553.http://dx.doi.org/10.1090/S0002-9947-04-03625-6
---------- VANCOUVER ----------
Grana, M., Turaev, V. Knot theory for self-indexed graphs. Trans. Am. Math. Soc. 2005;357(2):535-553.http://dx.doi.org/10.1090/S0002-9947-04-03625-6
