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Undergraduate Research at GANG
Summer 2000

Curves and Immersions

 The Figure "8" Sequence

This sequence is created when you add successive loops on the outside of the curve. The curves with an even number of crossings bound immersed manifolds on the sphere. In fact, as you proceed through the sequence the number of ways each curve bounds an immersed surface increases by approximately a factor of four. The curves with an odd number of crossing bound nothing.