In http://www.math.msu.edu/~akbulut/papers/akbulut.lec.pdf, which is a (still developed) set of lecture notes on 4-manifolds by Selman Akbulut, in section 1.5 there is a way to draw a non-orientable handle.
When reading this, I thought, this is just as cumbersome as drawing a 1-handle as a pair of balls (we now have the dotted circle for that, although (as Akbulut says) both notations have their advantages). For example when you have more than one nonoriented 1-handle.
My question is:
- Is there another, invariant way to depict nonorientation in a Kirby diagram ?
- As I understand it sofar, the notation used by Akbulut is mainly used for 1-handles. Is there a way to enhance Kirby diagrams such that nonorientation of 2-handles is also depicted ?