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Tight polyhedral submanifolds and tight triangulations / Wolfgang Kühnel.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1612.Publication details: New York : Springer-Verlag, 1995.Description: 1 online resource (122 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540494522
  • 3540494529
Subject(s): Additional physical formats: Print version:: Tight polyhedral submanifolds and tight triangulations.DDC classification:
  • 510 s 516.3/62 20
LOC classification:
  • QA3 .L28 no. 1612 QA670
Other classification:
  • 31.52
Online resources:
Contents:
1. Introduction and basic notions -- 2. Tight polyhedral surfaces -- 3. Tightness and k-tightness -- 4. (k -- 1)-connected 2k-manifolds -- 5. 3-manifolds and twisted sphere bundles -- 6. Connected sums and manifolds with boundary -- 7. Miscellaneous cases and pseudomanifolds.
Summary: 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.
Holdings
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Total holds: 0

Includes bibliographical references (pages (110-115) and index.

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.

1. Introduction and basic notions -- 2. Tight polyhedral surfaces -- 3. Tightness and k-tightness -- 4. (k -- 1)-connected 2k-manifolds -- 5. 3-manifolds and twisted sphere bundles -- 6. Connected sums and manifolds with boundary -- 7. Miscellaneous cases and pseudomanifolds.

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