Loading...
Please wait, while we are loading the content...
Similar Documents
The Heegaard Genus of Amalgamated 3-manifolds
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lackenby, Marc |
| Copyright Year | 2003 |
| Abstract | 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. MSC: 57N10 |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/math/0306320v1.pdf |
| Alternate Webpage(s) | https://ora.ox.ac.uk/objects/uuid:06e1c209-8e34-4a65-9995-10505fd9cbd0/datastreams/ATTACHMENT01 |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | Genus (mathematics) Pseudo brand of pseudoephedrine manifold |
| Content Type | Text |
| Resource Type | Article |
