Preparation:
1.) Construct a physical model of a surface of genus
2, and then draw onto this surface the completely connected
graph ("Kmax") of highest degree possible for a
genus-2 surface.
2.) Take a strip of thin paper or "onion-skin paper,"
mark it with a directional texture, then loop it into a
singly-twisted Moebius band. Bring your model to the
next class; we will do some comparisons to see in how many
different ways this task can be accomplished...
PPT
presentation.
Which ones are transformable into one another through a
"Regular Homotopy",
i.e., a deformation that allows surface regions to pass
through one another,
but does not allow any cuts, or tears, or formation of creases
or other singular points with infinite curvature.
(With this definition, it is possible to turn a sphere or a
torus inside out -- but it is not easy!).
