Talk Slides (2007-04-30.ualbany) tight-CES: Height Functions in CES

Height Functions in CES

In a CES, a (global) height function no longer makes sense, but one can define height functions locally.

Classically, a surface is tight provided every height function has exactly one maximum, and this corresponds to the two-piece property.

In CES, a surface with $\chi\le 0$ is tight provided every (local) height function has no maximum. In a sense, these surfaces have a "one-piece property".