Figures from this paper
figure 1 figure 2 figure 3 figure 4 figure 5 figure 6 figure 7 figure 8 figure 9 figure 10 figure 11 figure 12 figure 13 figure 14 figure 15 figure 16 figure 17 figure 18 figure 19 figure 20 figure 21 figure 22 figure 23 figure 24 figure 25 figure 26 figure 27 figure 28 figure 29 figure 30 figure 31 figure 32 figure 33 figure 34 figure 35 figure 36 figure 37 figure 38 figure 39 figure 40 figure 41 figure 42 figure 43 figure 44 figure 45
6 Citations
Computing a Link Diagram from Its Exterior
- MathematicsSoCG
- 2022
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
- Mathematics
- 2014
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
- Mathematics
- 2022
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…
A characterisation of alternating knot exteriors
- Mathematics
- 2015
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
- Mathematics
- 2022
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…
References
SHOWING 1-10 OF 14 REFERENCES
0-Efficient Triangulations of 3-Manifolds
- Mathematics
- 2002
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
- Mathematics
- 2005
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
- 2004
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
- 2006
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.
- 2001
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.
Tabulation of three-dimensional manifolds
- Computer Science
- 2005
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
- Engineering
- 1994
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…