Geodesic
Thin position for a connected sum of small knots
Rieck, Yo’av1 ; Sedgwick, Eric2
1Department of Mathematics, Nara Women’s University, Kitauoya Nishimachi, Nara 630-8506, Japan, Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA
2DePaul University, Department of Computer Science, 243 S. Wabash Ave. - Suite 401, Chicago, IL 60604, USA
Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 297-309
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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.

DOI : 10.2140/agt.2002.2.297
Keywords: 3–manifold, connected sum of knots, thin position

Rieck, Yo’av  1   ; Sedgwick, Eric  2

1 Department of Mathematics, Nara Women’s University, Kitauoya Nishimachi, Nara 630-8506, Japan, Department of Mathematics, University of Arkansas, Fayetteville, AR 72701, USA
2 DePaul University, Department of Computer Science, 243 S. Wabash Ave. - Suite 401, Chicago, IL 60604, USA 
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Rieck, Yo’av; Sedgwick, Eric. Thin position for a connected sum of small knots. Algebraic and Geometric Topology, Tome 2 (2002) no. 1, pp. 297-309. doi: 10.2140/agt.2002.2.297

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

[2] M Culler, C M Gordon, J Luecke, P B Shalen, Dehn surgery on knots, Ann. of Math. $(2)$ 125 (1987) 237

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

[4] C M Gordon, J Luecke, Knots are determined by their complements, J. Amer. Math. Soc. 2 (1989) 371

[5] D J Heath, T Kobayashi, Essential tangle decomposition from thin position of a link, Pacific J. Math. 179 (1997) 101

[6] K Morimoto, On tunnel number and connected sum of knots and links, from: "Geometric topology (Haifa, 1992)", Contemp. Math. 164, Amer. Math. Soc. (1994) 177

[7] K Morimoto, On the super additivity of tunnel number of knots, Math. Ann. 317 (2000) 489

[8] Y Rieck, Heegaard structures of manifolds in the Dehn filling space, Topology 39 (2000) 619

[9] Y Rieck, E Sedgwick, Finiteness results for Heegaard surfaces in surgered manifolds, Comm. Anal. Geom. 9 (2001) 351

[10] M Scharlemann, A Thompson, Thin position and Heegaard splittings of the 3–sphere, J. Differential Geom. 39 (1994) 343

[11] H Schubert, Über eine numerische Knoteninvariante, Math. Z. 61 (1954) 245

[12] J Schultens, Additivity of bridge numbers of knots, Sūrikaisekikenkyūsho Kōkyūroku (2001) 103

[13] A Thompson, Thin position and bridge number for knots in the 3–sphere, Topology 36 (1997) 505

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