Exceptional surgery curves in triangulated 3manifolds
Abstract
For the purposes of this paper, Dehn surgery along a curve K in a 3manifold M with slope r is `exceptional' if the resulting 3manifold M_K(r) is reducible or a solid torus, or the core of the surgery solid torus has finite order in the fundamental group of M_K(r). We show that, providing the exterior of K is irreducible and atoroidal, and the distance between r and the meridian slope is more than one, and a homology condition is satisfied, then there is (up to ambient isotopy) only a finite number of such exceptional surgery curves in a given compact orientable 3manifold M, with the boundary of M a (possibly empty) union of tori. Moreover, there is a simple algorithm to find all these surgery curves, which involves inserting tangles into the 3simplices of any given triangulation of M. As a consequence, we deduce some results about the finiteness of certain unknotting operations on knots in the 3sphere.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 July 1999
 arXiv:
 arXiv:math/9907093
 Bibcode:
 1999math......7093L
 Keywords:

 Mathematics  Geometric Topology;
 57N10;
 57M25
 EPrint:
 76 pages, 16 figures. For the same paper with better quality figures, visit http://www.dpmms.cam.ac.uk/~ml128