Eric Sedgwick

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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(More)
Simple curves on surfaces are often represented as sequences of intersections with a triangulation. However, topologists have much more succinct ways of representing simple curves such as normal coordinates which are exponentially more succinct than intersection sequences. Nevertheless, we show that the following two basic tasks of computational topology,(More)
To this end let X and Y be 3–manifolds with incompressible boundary homeomorphic to a connected surface F . It is not difficult to show that if HX and HY are Heegaard surfaces in X and Y then we can amalgamate these splittings to obtain a Heegaard surface in X∪F Y with genus equal to g(HX)+g(HY )−g(F) (see, for example, Schultens [14]). Letting g(X), g(Y),(More)
Here we present the results of the NSF-funded Workshop on Computational Topology, which met on June 11 and 12 in Miami Beach, Florida. This report identifies important problems involving both computation and topology. ∗Author affiliations: Marshall Bern, Xerox Palo Alto Research Ctr., bern@parc.xerox.com. David Eppstein, Univ. of California, Irvine, Dept.(More)
We show that every thin position for a connected sum of small knots is obtained in an obvious way: place each summand in thin position so that no two summands intersect the same level surface, then connect the lowest minimum of each summand to the highest maximum of the adjacent summand below. See Figure 1. AMS Classification 57M25; 57M27
Suppose that a three-manifold M contains infinitely many distinct strongly irreducible Heegaard splittings H + nK, obtained by Haken summing the surface H with n copies of the surface K. We show that K is incompressible. All known examples, of manifolds containing infinitely many irreducible Heegaard splittings, are of this form. We also give new examples(More)
We expect manifolds obtained by Dehn filling to inherit properties from the knot manifold. To what extent does that hold true for the Heegaard structure? We study four changes to the Heegaard structure that may occur after filling: (1) Heegaard genus decreases, (2) a new Heegaard surface is created, (3) a non-stabilized Heegaard surface destabilizes, and(More)