The Figure Eight Knot

  • George K. Francis


My final picture story is about visualizing how a knot complement fibers over the circle. This exercise of the imagination consists of filling the void of space, closed up by a single point at infinity to form the 3-sphere, with a continuous succession of surfaces spanning the knot. That is, through each point not on the curve, there will pass a unique copy of a surface whose boundary is the knot.


Line Pattern Klein Bottle Isotopy Class Dehn Twist Picture Plane 
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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • George K. Francis
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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