On the Seifert fibered space link group. (English) Zbl 1337.57037
Summary: We introduce generalized arrow diagrams and generalized Reidemeister moves for diagrams of links in Seifert fibered spaces. We give a presentation of the fundamental group of the link complement. As a corollary we are able to compute the first homology group of the complement and the twisted Alexander polynomials of the link.
MSC:
| 57M27 | Invariants of knots and \(3\)-manifolds (MSC2010) |
| 57M05 | Fundamental group, presentations, free differential calculus |
Keywords:
knots; links; Seifert fibered spaces; knot group; first homology group; twisted Alexander polynomialReferences:
| [1] | Bauval, A.; Hayat, C., L’anneau de cohomologie des variétés de Seifert, C. R. Math. Acad. Sci. Paris, 351, 81-85 (2013) · Zbl 1283.57024 |
| [2] | Bryden, J.; Lawson, T.; Pigott, B.; Zvengrowski, P., The integral homology of orientable Seifert fibered spaces, Topol. Appl., 127, 259-275 (2003) · Zbl 1025.57030 |
| [3] | Cattabriga, A.; Manfredi, E.; Mulazzani, M., On knots and links in lens spaces, Topol. Appl., 160, 430-442 (2013) · Zbl 1263.57004 |
| [4] | Diamantis, I.; Lambropoulou, S., Braid equivalence in 3-manifolds with rational surgery description, Topol. Appl., 194, 269-295 (2015) · Zbl 1353.57015 |
| [5] | Mroczkowski, M., Kauffman bracket skein module of the connected sum of two projective spaces, J. Knot Theory Ramif., 20, 651-675 (2011) · Zbl 1227.57019 |
| [6] | Mroczkowski, M., Kauffman bracket skein module of a family of prism manifolds, J. Knot Theory Ramif., 20, 651-675 (2011) · Zbl 1227.57019 |
| [7] | Mroczkowski, M.; Dabkowski, M. K., KBSM of the product of a disk with two holes and \(S^1\), Topol. Appl., 156, 1831-1849 (2009) · Zbl 1168.57010 |
| [8] | Orlik, P., Seifert Manifolds, Lecture Notes in Mathematics, vol. 291 (1972), Springer Verlag: Springer Verlag Berlin · Zbl 0263.57001 |
| [9] | Seifert, H.; Threlfall, W., Seifert and Threlfall: A Textbook of Topology, and Seifert: Topology of 3-Dimensional Fibered Spaces (1980), Academic Press: Academic Press New York · Zbl 0469.55001 |
| [10] | Turaev, V., Torsions of 3-Dimensional Manifolds, Progress in Mathematics, vol. 208 (2002), Birkhäuser Verlag: Birkhäuser Verlag Basel · Zbl 1012.57002 |
| [11] | Wada, M., Twisted Alexander polynomial for finitely presentable groups, Topology, 33, 241-256 (1994) · Zbl 0822.57006 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
