Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-26T03:13:10.086Z Has data issue: false hasContentIssue false
  • English
  • Français

Isotopy in surface complexes from the computational viewpoint

Published online by Cambridge University Press:  17 April 2009

John C. Stillwell
John C. Stillwell
Affiliation:
Department of Mathematics, Monash University, Clayton, Victoria.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is shown that the problem of deciding whether a curve in a finite surface complex is isotopic to a point is NP-complete. This contrasts with the recursively enumerable (RE)-completeness of the corresponding homotopy problem, and exhibits surface complexes as a common framework for NP-complete and RE-complete algorithmic problems.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 1 , January 1979 , pp. 1 - 6
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Boone, WiIliam W., Haken, W. and Poénaru, V., “On recursively unsolvable problems in topology and their classification”, Contributions to Mathematical Logic 37–74 (Proc. Logic Colloquium, Hannover, 1966. North-Holland, Amsterdam, 1968).Google Scholar
[2]Cook, Stephen A., “The complexity of theorem-proving procedures”, Proceedings of the Third Annual ACM Symposium on the Theory of Computing, Shaker Heights, Ohio, 1971, 151–158 (Association for Computing Machinery, New York, 1971).Google Scholar
[3]Dehn, M., “Über die Topologie des dreidimensionalen Raumes”, Math. Ann. 69 (1910), 137–168.CrossRefGoogle Scholar
[4]Karp, Richard M., “Reducibility among combinatorial problems”, Complexity of computer computations 85–103 (Proc. Sympos. Complexity of Computer Computations, New York, 1972. Plenum Press, New York, London, 1972).CrossRefGoogle Scholar
[5]Machtey, Michael and Young, Paul, An introduction to the general theory of algorithms (Theory of Computation Series, 2. Elsevier, New York, Shannon, 1978).Google Scholar
[6]Seifert, H. und Threlfall, W., Lehrbuch der Topologie (B.G. Teubner, Leipzig, Berlin, 1934. Reprinted Chelsea, New York),Google Scholar