Talk Slides (2007-04-30.ualbany) tight-CES: Otto's Conjectures

Otto's Conjectures

Otto conjectures that no smooth tight immersions of $\RP2$ with two handles exist in any CES, and that no tight immersion (smooth or polyhedral) of $\RP2$ with one handle exists in any CES.

It turns out that both these conjectures are false.

Indeed there exist tight embeddings of $\RP2$ with one handle in several CES, and immersions in all the others except one.

This gives us smooth tight embeddings or immersions of $\RP2$ with two handles in all CES but one, by the usual addition of handles.

As it happens, the final CES also allows a smooth immersion of this surface.