On the surface geometry of ordered sets.

S. Medhi T. Hashemi
This dissertation has two aims. The first is to study upward drawings of ordered sets on two-dimensional surfaces and secondly to study the geometry of the surfaces on which ordered sets can be drawn without crossing edges. Critical points, in particular, saddle points of ordered sets will play a decisive role. The Discrete Index Theorem, too, is fundamental. We present a characterization, in terms of critical points, of spherical ordered sets--ordered sets which have upward...
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