Algebraic and Geometric Topology 2 (2002), paper no. 14, pages 297-309.

Thin position for a connected sum of small knots

Yo'av Rieck, Eric Sedgwick

Abstract. 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.

Keywords. 3-manifold, connected sum of knots, thin position

AMS subject classification. Primary: 57M25. Secondary: 57M27.

DOI: 10.2140/agt.2002.2.297

E-print: arXiv:math.GT/0205125

Submitted: 7 January 2002. Accepted: 6 March 2002. Published: 24 April 2002.

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Yo'av Rieck, Eric Sedgwick
Department of Mathematics, Nara Women's University
Kitauoya Nishimachi, Nara 630-8506, Japan, and
Department of Mathematics, University of Arkansas
Fayetteville, AR 72701, USA
DePaul University, Department of Computer Science
243 S. Wabash Ave. - Suite 401, Chicago, IL 60604, USA

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