3 Critical Point Immersions-- Work in Progress
## 3 Critical Point Immersions-- Work in Progress

This pair of cross-sections is like the pair which bound section IV
of the torus immersion. The critical point which lies between them
would be a five-fold saddle (i.e. a starfish saddle?) The question
is, can these two curves be unlooped into circles without pinching
them? It turns out that they can't, because the one on the left has a
winding number of 3. So, if this pair of cross-sections can't
actually be unlooped, is there a similar pair which can? According to Prof. Banchoff's
article, there might be, and if there are, then the surface that
results has to be non-orientable.

All of that aside, what I *really* want to know is: what does the surface *look* like?

*Back*