### Non-isotopic Heegaard splittings of Seifert fibered spaces. With an appendix by R.Weidmann.

Bachman, David, Derby-Talbot, Ryan; (2006)

Algebraic & Geometric Topology

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Bachman, David, Derby-Talbot, Ryan; (2006)

Algebraic & Geometric Topology

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Chuichiro Hayashi, Koya Shimokawa (2001)

Revista Matemática Complutense

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We show that any Heegaard splitting of the pair of the solid torus (≅DxS) and its core loop (an interior point xS) is standard, using the notion of Heegaard splittings of pairs of 3-manifolds and properly imbedded graphs, which is defined in this paper.

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We study when an essential tangle decomposition of a satellite knot gives an essential tangle decomposition of the companion knot, that is, when the decomposing sphere can be isotoped to intersect the knotted solid torus identified with the pattern in meridian disks.

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