Geometriae Dedicata

, 143:7 | Cite as

Knots and k-width

Open Access
Original Paper


We investigate several natural invariants of curves and knots in \({\mathbb{R}^3}\) . These invariants generalize bridge number and width. As with bridge number, there are connections to the total curvature of a curve.


Knot theory Three-dimensional topology Thin position 2-width k-width 

Mathematics Subject Classification (2000)




Research of Joel Hass was supported in part by the NSF. Research of J. Hyam Rubinstein was supported in part by the Australian Research Council. Research of Abigail Thompson was supported in part by the NSF.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Joel Hass
    • 1
  • J. Hyam Rubinstein
    • 2
  • Abigail Thompson
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaDavisUSA
  2. 2.Department of Mathematics and StatisticsUniversity of MelbourneParkvilleAustralia

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