The toric cobordisms
| dc.creator | Mozgova, Alexandra | |
| dc.date | 2000-02-05 | |
| dc.date | 2004-11-15 | |
| dc.date.accessioned | 2026-07-25T22:38:40Z | |
| dc.description | A smooth closed 3-manifold $M$ fibered by tori $T^2$ is characterized by an element $ϕ\in GL(2,\mathbb{Z})$. We show that $M$ is the boundary of a 4-manifold fibered by tori over a surface such that the bundle structure on $M$ is the restriction of the bundle structure on the 4-manifold if and only if $ϕ$ is from the commutator subgroup $(GL(2,\mathbb{Z}))'$. The notions of oriented and unoriented cobordisms in the class of closed 3-manifolds fibered by tori are introduced. It turns out that in this case the cobordisms form a group, namely $\mathbb{Z}_{12}$ in the oriented case and $\mathbb{Z}_{2}\oplus\mathbb{Z}_{2}$ in the unoriented one. When the surface on the base of oriented cobordism is orientable, it is shown that its minimal genus can be calculated by Culler's algorithm. | |
| dc.description | 3 pages, final version | |
| dc.identifier | https://arxiv.org/abs/math/0002043 | |
| dc.identifier | http://arxiv.org/abs/math/0002043 | |
| dc.identifier | Proc. Amer. Math. Soc. 132 (2004), no. 1, 299--303 | |
| dc.identifier.uri | https://dspace.dare.co.zw/handle/123456789/91102 | |
| dc.subject | Algebraic Topology | |
| dc.subject | primary 57M50, 57M07; secondary 55R10 | |
| dc.title | The toric cobordisms | |
| dc.type | text |