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Tight Polyhedral Submanifolds and Tight Triangulations

  • Book
  • © 1995

Overview

Authors:
  1. Wolfgang Kühnel
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1612)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VII
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  2. Introduction and basic notions

    • Wolfgang Kühnel
    Pages 1-5

  3. Tight polyhedral surfaces

    • Wolfgang Kühnel
    Pages 6-40

  4. Tightness and k-tightness

    • Wolfgang Kühnel
    Pages 41-55

  5. (k−1)-connected 2k-manifolds

    • Wolfgang Kühnel
    Pages 56-77

  6. 3-manifolds and twisted sphere bundles

    • Wolfgang Kühnel
    Pages 78-84

  7. Connected sums and manifolds with boundary

    • Wolfgang Kühnel
    Pages 85-94

  8. Miscellaneous cases and pseudomanifolds

    • Wolfgang Kühnel
    Pages 95-109

  9. Back Matter

    Pages 110-122
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Tight Polyhedral Submanifolds and Tight Triangulations

  • Authors: Wolfgang Kühnel

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0096341

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1995

  • Softcover ISBN: 978-3-540-60121-0Published: 18 September 1995

  • eBook ISBN: 978-3-540-49452-2Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VIII, 128

  • Topics: Differential Geometry, Manifolds and Cell Complexes (incl. Diff.Topology)

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