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Thin position for a connected sum of small knots

Yo'av Rieck and Eric Sedgwick

Algebraic & Geometric Topology 2 (2002) 297–309

DOI: 10.2140/agt.2002.2.297

arXiv: math.GT/0205125
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
Mathematical Subject Classification

Primary: 57M25

Secondary: 57M27
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Publication

Received: 7 January 2002
Accepted: 6 March 2002
Published: 24 April 2002
Authors
Yo'av Rieck
Department of Mathematics
Nara Women's University
Kitauoya Nishimachi
Nara 630-8506
Japan
Eric Sedgwick
DePaul University
Department of Computer Science
243 S. Wabash Ave. - Suite 401
Chicago, IL 60604
USA