The Heegaard genus of amalgamated 3-manifolds
| dc.creator | Lackenby, Marc | |
| dc.date | 2003-06-23 | |
| dc.date.accessioned | 2026-07-07T04:59:06Z | |
| dc.date.available | 2026-07-07T04:59:06Z | |
| dc.description | Let M and M' be simple 3-manifolds, each with connected boundary of genus at least two. Suppose that M and M' are glued via a homeomorphism between their boundaries. Then we show that, provided the gluing homeomorphism is `sufficiently complicated', the Heegaard genus of the amalgamated manifold is completely determined by the Heegaard genus of M and M' and the genus of their common boundary. Here, a homeomorphism is `sufficiently complicated' if it is the composition of a homeomorphism from the boundary of M to some surface S, followed by a sufficiently high power of a pseudo-Anosov on S, followed by a homeomorphism to the boundary of M'. The proof uses the hyperbolic geometry of the amalgamated manifold, generalised Heegaard splittings and minimal surfaces. | |
| dc.description | 7 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0306320 | |
| dc.identifier | http://arxiv.org/abs/math/0306320 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67851 | |
| dc.subject | Geometric Topology | |
| dc.subject | 57N10 | |
| dc.title | The Heegaard genus of amalgamated 3-manifolds | |
| dc.type | text |