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.

Keywords

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)

Publish with us

Policies and ethics

Authors:

Sections

Buy it now

Buying options

Other ways to access

Table of contents (7 chapters)

Front Matter

Introduction 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

Back Matter

About this book