Embedded spheres in S^2\times S^1#...#S^2\times S^1
| dc.creator | Gadgil, Siddhartha | |
| dc.date | 2004-10-04 | |
| dc.date.accessioned | 2026-07-07T05:12:49Z | |
| dc.date.available | 2026-07-07T05:12:49Z | |
| dc.description | We give an algorithm to decide which elements of pi_2(S^2\times S^1#...#S^2\times S^1) can be represented by embedded spheres. Such spheres correspond to splittings of the free group on k generators. Equivalently our algorithm decides whether, for a handlebody N, an element in pi_2(N,\partial N) can be represented by an embedded disc. We also give an algorithm to decide when classes in $π_2(S^2\times S^1#...#S^2\times S^1)$ can be represented by disjoint embedded spheres. We introduce the splitting complex of a free group which is analogous to the complex of curves of a surface. We show that the splitting complex of the free group on k generators embeds in the complex of curves of a surface of genus $k$ as a quasi-convex subset. | |
| dc.description | 8 pages | |
| dc.identifier | https://arxiv.org/abs/math/0410047 | |
| dc.identifier | http://arxiv.org/abs/math/0410047 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72723 | |
| dc.subject | Geometric Topology | |
| dc.subject | Group Theory | |
| dc.subject | 57M05 ; 57M07, 20E06 | |
| dc.title | Embedded spheres in S^2\times S^1#...#S^2\times S^1 | |
| dc.type | text |