The topological interpretation of the core group of a surface in S^4
| dc.creator | Przytycki, Jozef H. | |
| dc.creator | Rosicki, Witold | |
| dc.date | 2004-03-26 | |
| dc.date.accessioned | 2026-07-07T05:06:49Z | |
| dc.date.available | 2026-07-07T05:06:49Z | |
| dc.description | We give a topological interpretation of the core group invariant of a surface embedded in S^4. We show that the group is isomorphic to the free product of the fundamental group of the double branch cover of S^4 with the surface as a branched set, and the infinite cyclic group. We present a generalization for unoriented surfaces, for other cyclic branched covers, and other codimension two embeddings of manifolds in spheres. The method of computing the fundamental group of n-fold cyclic branched covers is related to the one described in R.H.Crowell, The derived group of a permutation representation, Adv. in Math. 53(1), 1984, 99--124. We use these computations in recent papers: http://front.math.ucdavis.edu/math.GT/0302098 http://front.math.ucdavis.edu/math.GT/0309140 | |
| dc.description | 9 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/math/0403475 | |
| dc.identifier | http://arxiv.org/abs/math/0403475 | |
| dc.identifier | Canad. Math. Bull., 45(1), 2002, pp. 131-137 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70620 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57 Q45 (Primary) 57 M12, 57 M05 (Secondary) | |
| dc.title | The topological interpretation of the core group of a surface in S^4 | |
| dc.type | text |