
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.

