The Heegaard genus of amalgamated 3-manifolds

Details The Heegaard genus of amalgamated 3-manifolds The Heegaard genus of amalgamated 3-manifolds

2003-06-23

arxiv.org/abs/math/0306320v1

Mathematics

Geometric Topology

7 pages, 2 figures

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

The Heegaard genus of amalgamated 3-manifolds does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Heegaard genus of amalgamated 3-manifolds, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Heegaard genus of amalgamated 3-manifolds will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-513722