Tight Polyhedral Submanifolds and Tight Triangulations

Download or read book Tight Polyhedral Submanifolds and Tight Triangulations written by Wolfgang Kühnel and published by Springer. This book was released on 2006-11-14 with total page 129 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is an introduction and a monograph about tight polyhedra. The treatment of the 2-dimensional case is self- contained and fairly elementary. It would be suitable also for undergraduate seminars. Particular emphasis is given to the interplay of various special disciplines, such as geometry, elementary topology, combinatorics and convex polytopes in a way not found in other books. A typical result relates tight submanifolds to combinatorial properties of their convex hulls. The chapters on higher dimensions generalize the 2-dimensional case using concepts from combinatorics and topology, such as combinatorial Morse theory. A number of open problems is discussed.