Some PL functions on surfaces are not height functions
S. Yu. Tarasov, M. Vyalyi · 1997
We find some obstructions for piecewise-linear (PL) functions defined on two-dimensional closed compact manifolds (surfaces) to be heightfunctionsin R3 andprove existenceof some non-height PL tiutctions.On the other hand we prove thatall PL functions on a sphereare heightfunctions.