A trivial knot whose spanning disks have exponential size

Subscribe (Full Service)


	Search: The ACM Digital Library The Guide

	Feedback

A trivial knot whose spanning disks have exponential size

Full text

Pdf (605 KB)

Source

Annual Symposium on Computational Geometry archive
Proceedings of the sixth annual symposium on Computational geometry table of contents

Berkley, California, United States

Pages: 139 - 147

Year of Publication: 1990

ISBN:0-89791-362-0

Author

Jack Snoeyink

Department of Computer Science, Stanford University

Sponsors

SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

Publisher

ACM New York, NY, USA

Bibliometrics

Downloads (6 Weeks): 3, Downloads (12 Months): 10, Citation Count: 1

Additional Information:

abstract references cited by index terms collaborative colleagues

Tools and Actions:	Request Permissions Review this Article Save this Article to a Binder Display Formats: BibTeX EndNote ACM Ref

DOI Bookmark:	Use this link to bookmark this Article: http://doi.acm.org/10.1145/98524.98555 What is a DOI?

ABSTRACT

If a closed curve in space is a trivial knot (intuitively, one can untie it without cutting) then it is the boundary of some disk with no self-intersections. In this paper we investigate the minimum number of faces of a polyhedral spanning disk of a polygonal knot with n segments. We exhibit a knot whose minimal spanning disk has exp(cn) faces, for some positive constant c.

REFERENCES

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

	1	M. A. Armstrong. Basic Topology. McGraw- Hill, London, 1979.
	2	H. S. M. Coxeter and W. O. J. Moser. Ge'nerators and Relations for Discrete Groups. Springer Verlag, third edition, 1972.
	3	Richard H. Crowell and Ralph H. Fox. Introduction to Knot Theory. Blaisdell Publishing Co., New York, 1965.
	4	Mike Fellows. Problem Corner: 6. The complexity of knot triviality and the Arf invariant. In Graphs and Algorithms: Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference, volume 89 of Contemporary Mathematics~ pages 189-190. American Mathematical Society, 1989.
	5	Wolfgang Haken. Theorie der Normalfl~chen: Ein Isotopiekriterium fiir den Kreisknoten. Acta Mathematica, 105:245-375, 1961.
	6	Dale Rolfsen. Knots and Links. Publish or Perish, Berkeley, 1976.
	7	C. P. Rourke and B. J. Sanderson. Introduction to Piecewise-Linear Topology. Springer Verlag, 1972.
	8	Horst Schubert. Bestimmung der Primfaktorzerlegung yon Verkettungen. Mathematische Zeitschrifl, 76:116-148, 1961.