Talk Slides (2007-04-30.ualbany) tight-CES: Smoothable Projective Plane with Two Handles

Smoothable $\RP2$ with Two Handles

Every one of the models of the Klein bottles with one handle that we produced earlier has a monkey saddle at the point where the two ends of the handle meet at the center.

By replacing the saddle as we just descibed, we obtain $\RP2$ with two handles in every CES. The resulting model is smoothable in each case.