most recent 30 from http://mathoverflow.net 2013-06-18T06:07:35Z http://mathoverflow.net/feeds/question/110817 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/110817/pl-surface-projections-is-there-a-theory-of-folds-and-cusps johnwbarrett 2012-10-27T08:41:07Z 2012-10-27T08:41:07Z

<p>For smooth surfaces, the generic singularities of a map of one surface to another are folds and cusps (Whitney). It is a standard result in singularity theory that the generic isotopy of such a map is an isotopy of the projection plane punctuated by a sequence of local moves. The moves are one of three types in which a two cusps either appear or disappear.</p> <p>Has the analogous theory for PL surfaces and maps been developed? I've been unable to find it using the usual search tools.</p>