Friday, January 16, 2015

Morse theory and torus level sets

The sets of fixed height (level curves) on the torus standing on end change topologically when the height hits the hole.  The bottom level set is a point, followed by one loop between the bottom at the hole, a figure eight at exactly the where the hole starts,  two loops inside the hole, and then everything in reverse order on the top half ending in a point at the very top. This is a popular illustrative example in the study of Morse theory.


Things looked kind of a mess before removal from the build plate, but that turned out to be the dual build fence rather than the model.

No comments:

Post a Comment