Tight polyhedral submanifolds and tight triangulations

Wolfgang Kühnel

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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  • 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.

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書名 Tight polyhedral submanifolds and tight triangulations
著作者等 Kühnel, Wolfgang
Kuhnel Wolfgang
シリーズ名 Lecture notes in mathematics
出版元 Springer-Verlag
刊行年月 c1995
ページ数 122 p.
大きさ 24 cm
ISBN 354060121X
NCID BA25891640
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言語 英語
出版国 ドイツ