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.