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2-bridgeθ-curves inS 3

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
108
Issue
3
Identifiers
DOI: 10.1016/s0166-8641(99)00139-x
Keywords
  • Spatial Graph
  • θ-Curve
  • Bridge Number

Abstract

Abstract In [Math. Z. 61 (1954) 245], Schubert introduced an invariant of knots in the 3-sphere, called the bridge number, and Goda extended this invariant to θ-curves in [Topology Appl. 79 (1997) 177]. It is known that knots with bridge number 2 are prime. However we show in this paper that θ-curves with bridge number 2 are not always prime. Actually we give a necessary and sufficient condition for θ-curves to be nonprime with bridge number 2.

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