Decision problems in the space of Dehn fillings

Details Decision problems in the space of Dehn fillings Decision problems in the space of Dehn fillings

1998-11-06

arxiv.org/abs/math/9811031v1

Mathematics

Geometric Topology

70 pages, 24 figures

Scientific paper

In this paper, we use normal surface theory to study Dehn filling on a knot-manifold. First, it is shown that there is a finite computable set of slopes on the boundary of a knot-manifold that bound normal and almost normal surfaces in a one-vertex triangulation of that knot-manifold. This is combined with existence theorems for normal and almost normal surfaces to construct algorithms to determine precisely which manifolds obtained by Dehn filling: 1) are reducible, 2) contain two--sided incompressible surfaces, 3) are Haken, 4) fiber over the circle, 5) are the 3--sphere, and 6) are a lens space. Each of these algorithms is a finite computation. Moreover, in the case of essential surfaces, we show that the topology of the filled manifolds is strongly reflected in the triangulation of the knot-manifold. If a filled manifold contains an essential surface then the knot-manifold contains an essential vertex solution that caps off to an essential surface of the same type in the filled manifold. (Vertex solutions are the premier class of normal surface and are computable.)

Affiliated with

Also associated with

No associations

Rating

Decision problems in the space of Dehn fillings 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 Decision problems in the space of Dehn fillings, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Decision problems in the space of Dehn fillings will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-584563