Algebraic & Geometric Topology

Thin position for a connected sum of small knots

Yo’av Rieck and Eric Sedgwick

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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.

Article information

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

3–manifold connected sum of knots thin position


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.

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