On representations of 2-bridge knot groups in quaternion algebras.
| dc.contributor.author | Hilden, Hugh Michael | |
| dc.contributor.author | Lozano Imízcoz, María Teresa | |
| dc.contributor.author | Montesinos Amilibia, José María | |
| dc.date.accessioned | 2023-06-20T03:32:58Z | |
| dc.date.available | 2023-06-20T03:32:58Z | |
| dc.date.issued | 2011-10-10 | |
| dc.description.abstract | Representations of two bridge knot groups in the isometry group of some complete Riemannian 3-manifolds as E3 (Euclidean 3-space), H3 (hyperbolic 3-space) and E2, 1 (Minkowski 3-space), using quaternion algebra theory, are studied. We study the different representations of a 2-generator group in which the generators are send to conjugate elements, by analyzing the points of an algebraic variety, that we call the variety of affine c-representations ofG. Each point in this variety corresponds to a representation in the unit group of a quaternion algebra and their affine deformations. | |
| dc.description.department | Depto. de Álgebra, Geometría y Topología | |
| dc.description.faculty | Fac. de Ciencias Matemáticas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MTM2007-67908-C02-01 and MTM2010-21740-C02-02. | |
| dc.description.sponsorship | MTM2006-00825 and MTM2009-07030. | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/21529 | |
| dc.identifier.doi | 10.1142/S0218216511009224 | |
| dc.identifier.issn | 0218-2165 | |
| dc.identifier.officialurl | http://www.worldscientific.com/doi/pdf/10.1142/S0218216511009224 | |
| dc.identifier.relatedurl | http://www.worldscientific.com/ | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/43832 | |
| dc.issue.number | 10 | |
| dc.journal.title | Journal Of Knot Theory And Its Ramifications | |
| dc.language.iso | eng | |
| dc.page.final | 1419 | |
| dc.page.initial | 1419 | |
| dc.publisher | World Scientific PublCo | |
| dc.relation.projectID | 2007-67908-C02-01 | |
| dc.relation.projectID | 2010-21740-C02-02 | |
| dc.relation.projectID | 2006-00825 | |
| dc.relation.projectID | 2009-07030 | |
| dc.rights.accessRights | restricted access | |
| dc.subject.cdu | 515.162.8 | |
| dc.subject.keyword | Quaternion algebra | |
| dc.subject.keyword | representation | |
| dc.subject.keyword | knot group | |
| dc.subject.ucm | Geometria algebraica | |
| dc.subject.unesco | 1201.01 Geometría Algebraica | |
| dc.title | On representations of 2-bridge knot groups in quaternion algebras. | |
| dc.type | journal article | |
| dc.volume.number | 20 | |
| dcterms.references | G. W. Brumfiel and H. M. Hilden, (SL)2 Representations of Finitely Presented Groups, Contemporary Mathematics, Vol. 187 (American Mathematical Society, Providence, RI, 1995). V. Charette, T. Drumm, W. Goldman and M. Morrill, Complete flat affine and Lorentzian manifolds, Geom. Dedicata 97 (2003) 187–198. Special volume dedicated to the memory of Hanna Miriam Sandler (1960–1999). D. Cooper and D. D. Long, Remarks on the A-polynomial of a knot, J. Knot Theory Ramifications 5(5) (1996) 609–628. ) R. H. Crowell and R. H. Fox, Introduction to Knot Theory, based upon lectures given at Haverford College under the Philips Lecture Program (Ginn and Co., Boston, MA, 1963). M. Culler and P. B. Shalen, Varieties of group representations and splittings of 3-manifolds, Ann. of Math. (2) 117(1) (1983) 109–146. G. de Rham, Introduction aux polynômes d'un nœud, Enseign. Math. (2) 13 (1967) 187–194. D. Fried and W. M. Goldman, Three-dimensional affine crystallographic groups, Adv. Math. 47(1) (1983) 1–49. W. M. Goldman, Nonstandard Lorentz space forms, J. Differential Geom. 21(2) (1985) 301–308. F. González-Acu~na and J. M. Montesinos-Amilibia, On the character variety of group representations in SL(2,C) and PSL(2,C), Math. Z. 214(4) (1993) 627–652. H. M. Hilden, M. T. Lozano and J. M. Montesinos-Amilibia, On the character variety of group representations of a 2-bridge link p/3 into PSL(2,C), Bol. Soc. Mat. Mexicana (2) 37(1–2) (1992) 241–262. Papers in honor of José Adem (in Spanish). H. M. Hilden, M. T. Lozano and J. M. Montesinos-Amilibia, On the arithmetic 2-bridge knots and link orbifolds and a new knot invariant, J. Knot Theory Ramifications 4(1) (1995) 81–114. H. M. Hilden, M. T. Lozano and J. M. Montesinos-Amilibia, Character varieties and peripheral polynomials of a class of knots, J. Knot Theory Ramifications 12(8) (2003) 1093–1130. H. M. Hilden, M. T. Lozano and J. M. Montesinos-Amilibia, Peripheral polynomials of hyperbolic knots, Topol. Appl. 150(1–3) (2005) 267–288. H. M. Hilden, M. T. Lozano and J. M. Montesinos-Amilibia, On the affine representations of the trefoil knot group, preprint (2010), arXiv:1003.3554 [math.GT]. T. Y. Lam, The Algebraic Theory of Quadratic Forms, Mathematics Lecture Note Series (W. A. Benjamin, Reading, MA, 1973). R. Riley, Nonabelian representations of 2-bridge knot groups, Q. J. Math. (2) 35(138) (1984) 191–208. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 7097502e-a5b0-4b03-b547-bc67cda16ae2 | |
| relation.isAuthorOfPublication.latestForDiscovery | 7097502e-a5b0-4b03-b547-bc67cda16ae2 |
Download
Original bundle
1 - 1 of 1