Abstract
Guillemin and Zara (Duke Math J 107(2):283–349, 2001) described an analogue of Morse theory on a certain class of 1-skeleta including all those coming from simple polytopes. In this paper we extend the methods of Guillemin and Zara to a larger class of 1-skeleta including all those coming from simple polytopes and their 1-skeleton projections. As an application of these methods we prove a lifting result which yields an intrinsic characterization of 1-skeleton projections of simple polytopes.
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