Tight Polyhedral Submanifolds and Tight Triangulations

Wolfgang Kühnel (auth.)9783540601210, 354060121X

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.

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Table of contents :
Introduction and basic notions….Pages 1-5
Tight polyhedral surfaces….Pages 6-40
Tightness and k -tightness….Pages 41-55
( k −1)-connected 2 k -manifolds….Pages 56-77
3-manifolds and twisted sphere bundles….Pages 78-84
Connected sums and manifolds with boundary….Pages 85-94
Miscellaneous cases and pseudomanifolds….Pages 95-109