Algebraic & Geometric Topology

Thin position for a connected sum of small knots

Yo’av Rieck and Eric Sedgwick

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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.

Article information

Source
Algebr. Geom. Topol., Volume 2, Number 1 (2002), 297-309.

Dates
Received: 7 January 2002
Accepted: 6 March 2002
First available in Project Euclid: 21 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513882694

Digital Object Identifier
doi:10.2140/agt.2002.2.297

Mathematical Reviews number (MathSciNet)
MR1917054

Zentralblatt MATH identifier
0991.57004

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds

Keywords
3–manifold connected sum of knots thin position

Citation

Rieck, Yo’av; Sedgwick, Eric. Thin position for a connected sum of small knots. Algebr. Geom. Topol. 2 (2002), no. 1, 297--309. doi:10.2140/agt.2002.2.297. https://projecteuclid.org/euclid.agt/1513882694


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