0708-1300/Class notes for Tuesday, January 29

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Two Covering Spaces

0708-1300-DoubleCover.png 0708-1300-FigureEightSeifert.jpg
Mathematica code:
ParametricPlot3D[
  {
    {r Cos[2t], r Sin[2t], 4 + Cos[t]},
    {r Cos[t], r Sin[t], 0},
    PlotPoints -> {49, 2}
  },
  {t, 0, 2Pi}, {r, 1, 3}
]
Seifert surface of the Figure Eight Knot, drawn using Jack van Wijk's amazing SeifertView.

14 Covering Spaces

14 further covering spaces can be found on page 58 of Hatcher's book.