Year of Publication
Doctor of Philosophy (PhD)
Arts and Sciences
Dr. Carl W Lee
We generalize bistellar operations (often called flips) on simplicial manifolds to a notion of general flips on PL-spheres. We provide methods for computing the cd-index of these general flips, which is the change in the cd-index of any sphere to which the flip is applied. We provide formulas and relations among flips in certain classes, paying special attention to the classic case of bistellar flips. We also consider questions of "flip-connecticity", that is, we show that any two polytopes in certain classes can be connected via a sequence of flips in an appropriate class.
Wells, Daniel J., "GENERAL FLIPS AND THE CD-INDEX" (2010). University of Kentucky Doctoral Dissertations. 33.