Computing a Link Diagram from Its Exterior
A knot is a circle piecewise-linearly embedded into the 3-sphere. The topology of a knot is intimately related to that of its exterior, which is the complement of an open regular neighborhood of the…
Bounds for the genus of a normal surface
This paper gives sharp linear bounds on the genus of a normal surface in a triangulated compact, orientable 3--manifold in terms of the quadrilaterals in its cell decomposition---different bounds…
Complexity of 3-manifolds obtained by Dehn filling
Let M be a compact 3–manifold with boundary a single torus. We present upper and lower complexity bounds for closed 3–manifolds obtained as even Dehn ﬁllings of M . As an application, we characterise…
Efficient triangulations and boundary slopes
A characterisation of alternating knot exteriors
We give a topological characterisation of alternating knot exteriors based on the presence of special spanning surfaces. This shows that alternating is a topological property of the knot exterior and…
Normal surfaces and colored Khovanov homology
We show that colored Khovanov homology detects classes of essential surfaces as a direct analogue of the slope conjectures for the colored Jones polynomial. We do this by identifying certain…
SHOWING 1-10 OF 14 REFERENCES
0-Efficient Triangulations of 3-Manifolds
efficient triangulations of 3-manifolds are defined and studied. It is shown that any triangulation of a closed, orientable, irreducible 3-manifold M can be modified to a 0-efficient triangulation…
Angle structures and normal surfaces
Let M be the interior of a compact 3-manifold with boundary, and let T be an ideal triangulation of M. This paper describes necessary and sufficient conditions for the existence of angle structures,…
FACE PAIRING GRAPHS AND 3-MANIFOLD ENUMERATION
- Mathematics, Computer Science
Constraints upon the combinatorial structure of such a triangulation that can be deduced from its face pairing graph are presented and applied to the enumeration of closed minimal ℙ2-irreducible 3-manifold triangulations, leading to a significant improvement in the performance of the enumerations algorithm.
FINDING PLANAR SURFACES IN KNOT- AND LINK-MANIFOLDS
- Computer Science
It is shown that given any link-manifold, there is an algorithm to decide if the manifold contains an embedded, essential planar surface; if it does, the algorithm will construct one. Two similar…
Three-Manifolds Having Complexity At Most 9
- MathematicsExp. Math.
An algorithm is described which has enabled us to give a complete list, without repetitions, of all closed oriented irreducible three-manifolds of complexity up to 9, and it is proved that there are surprisingly few such manifolds up to complexity 9.
Approximating cellular maps by homeomorphisms
Tabulation of three-dimensional manifolds
- Computer Science
The theoretical foundations of the listing algorithm and the recognition algorithm are presented and a survey of results concerning the practical tabulation of three-dimensional manifolds is given.
THIN POSITION AND THE RECOGNITION PROBLEM FOR S3
An improved protective carrier for microcircuit devices having beam leads wherein a compressible member is disposed on the carrier base beneath and overlapping the periphery of an aperture in a…
Polyhedral minimal surfaces, Heegaard splittings, and decision problems for 3-dimensional manifolds