Geodesic
The size of triangulations supporting a given link
King, Simon A1
1 Institut de Recherche Mathématique Avancée, Strasbourg, France
Geometry & topology, Tome 5 (2001) no. 1, pp. 369-398.

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

Let T be a triangulation of S3 containing a link L in its 1–skeleton. We give an explicit lower bound for the number of tetrahedra of T in terms of the bridge number of L. Our proof is based on the theory of almost normal surfaces.

DOI : 10.2140/gt.2001.5.369
Keywords: link, triangulation, bridge number, Rubinstein–Thompson algorithm, normal surfaces

King, Simon A 1

1 Institut de Recherche Mathématique Avancée, Strasbourg, France 
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King, Simon A. The size of triangulations supporting a given link. Geometry & topology, Tome 5 (2001) no. 1, pp. 369-398. doi : 10.2140/gt.2001.5.369. http://geodesic.mathdoc.fr/articles/10.2140/gt.2001.5.369/

[1] S Armentrout, Knots and shellable cell partitionings of $S^3$, Illinois J. Math. 38 (1994) 347

[2] G Burde, H Zieschang, Knots, de Gruyter Studies in Mathematics 5, Walter de Gruyter Co. (1985)

[3] R Ehrenborg, M Hachimori, Non-constructible complexes and the bridge index, European J. Combin. 22 (2001) 475

[4] R Furch, Zur Grundlegung der kombinatorischen Topologie, Abh. Math. Sem. Hamb. Univ. 3 (1924) 60

[5] D Gabai, Foliations and the topology of 3-manifolds III, J. Differential Geom. 26 (1987) 479

[6] R E Goodrick, Non-simplicially collapsible triangulations of $I^n$, Proc. Cambridge Philos. Soc. 64 (1968) 31

[7] M Hachimori, G M Ziegler, Decompositions of simplicial balls and spheres with knots consisting of few edges, Math. Z. 235 (2000) 159

[8] W Haken, Über das Homöomorphieproblem der 3–Mannigfaltigkeiten I, Math. Z. 80 (1962) 89

[9] W Haken, Some results on surfaces in 3–manifolds, from: "Studies in Modern Topology", Math. Assoc. Amer. (distributed by Prentice-Hall, Englewood Cliffs, N.J.) (1968) 39

[10] J Hass, J C Lagarias, The number of Reidemeister moves needed for unknotting, J. Amer. Math. Soc. 14 (2001) 399

[11] G Hemion, The classification of knots and 3–dimensional spaces, Oxford Science Publications, The Clarendon Press Oxford University Press (1992)

[12] S A King, The size of triangulations supporting a given link, Geom. Topol. 5 (2001) 369

[13] S A King, How to make a triangulation of $S^3$ polytopal, Trans. Amer. Math. Soc. 356 (2004) 4519

[14] H Kneser, Geschlossene Flächen in dreidimensionalen Mannigfaltigkeiten, Jahresber. Deut. Math. Ver. 38248

[15] W B R Lickorish, Unshellable triangulations of spheres, European J. Combin. 12 (1991) 527

[16] S V Matveev, Algorithms for the recognition of the three-dimensional sphere (after A Thompson), Mat. Sb. 186 (1995) 69

[17] S V Matveev, On the recognition problem for Haken 3–manifolds, from: "Proceedings of the Workshop on Differential Geometry and Topology (Palermo, 1996)" (1997) 131

[18] A Mijatović, Simplifying triangulations of $S^3$, Pacific J. Math. 208 (2003) 291

[19] J H Rubinstein, Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3–dimensional manifolds, from: "Geometric topology (Athens, GA, 1993)", AMS/IP Stud. Adv. Math. 2, Amer. Math. Soc. (1997) 1

[20] M Scharlemann, A Thompson, Thin position for 3–manifolds, from: "Geometric topology (Haifa, 1992)", Contemp. Math. 164, Amer. Math. Soc. (1994) 231

[21] A Schrijver, Theory of linear and integer programming, Wiley-Interscience Series in Discrete Mathematics, John Wiley Sons Ltd. (1986)

[22] A Thompson, Thin position and the recognition problem for $S^3$, Math. Res. Lett. 1 (1994) 613

[23] A Thompson, Algorithmic recognition of 3–manifolds, Bull. Amer. Math. Soc. $($N.S.$)$ 35 (1998) 57

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