Tight Polyhedral Submanifolds and Tight Triangulations / Edition 1

by Wolfgang Kïhnel

Overview

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.

Product Details

ISBN-13:	9783540601210
Publisher:	Springer Berlin Heidelberg
Publication date:	10/27/1995
Series:	Lecture Notes in Mathematics , #1612
Edition description:	1995
Pages:	128
Product dimensions:	6.10(w) x 9.25(h) x 0.01(d)

Table of Contents

and basic notions.- Tight polyhedral surfaces.- Tightness and k-tightness.- (k-1)-connected 2k-manifolds.- 3-manifolds and twisted sphere bundles.- Connected sums and manifolds with boundary.- Miscellaneous cases and pseudomanifolds.