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Heegaard splittings of exteriors of two bridge knots

Tsuyoshi Kobayashi

Geometry & Topology 5 (2001) 609–650

arXiv: math.GT/0101148

Abstract

In this paper, we show that, for each non-trivial two bridge knot K and for each g 3, every genus g Heegaard splitting of the exterior E(K) of K is reducible.

Keywords
two bridge knot, Heegaard splitting
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M05
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Publication
Received: 23 February 2001
Accepted: 5 June 2001
Published: 27 June 2001
Proposed: Cameron Gordon
Seconded: Joan Birman, Robion Kirby
Authors
Tsuyoshi Kobayashi
Department of Mathematics
Nara Women’s University
Kita-Uoya Nishimachi
Nara 630-8506
Japan