Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-23T22:09:10.940Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsolvability of the knot problem for surface complexes

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 polygonal curve c in a finite surface complex K is knotted in K is complete recursively enumerable, and hence unsolvable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 20 , Issue 1 , January 1979 , pp. 131 - 137
Copyright
Copyright © Australian Mathematical Society 1979

References

[1]Alexander, J.W., “Some problems in topology”, Verhandlungen des Internationalen Mathematiker-Kongresses, Zürich, 1932. Band I. Bericht und Allgemeine Vortrage, 249–257 (Orell Füssli, Zürich, Leipzig, ND[1933]; Kraus Reprint Limited, Nendeln, 1967).Google Scholar
[2]Dehn, M., “Über die Topologie des dreidimensionalen Raumes”, Math. Ann. 69 (1910), 137–168.CrossRefGoogle Scholar
[3]Haken, Wolfgang, “Connections between topological and group theoretical decision problems”, Word problems, decision problems and the Burnside problem in group theory, 427–441 (Studies in Logic and the Foundations of Mathematics,. North-Holland, Amsterdam, London, 1973).CrossRefGoogle Scholar
[4]Savitch, Walter J., “Relationship between nondeterministic and deterministic tape complexities”, J. Computer System Sci. 4 (1970), 177–192.CrossRefGoogle Scholar
[5]Seifert, H. und Threlfall, W., Lehrbuch der Topologie (B.G. Teubner, Leipzig, Berlin, 1934. Reprinted Chelsea, New York, 1947)Google Scholar
[6]Stillwell, John C., “Isotopy in surface complexes from the computational viewpoint”, Bull. Austral. Math. Soc. 20 (1979), 1–6.CrossRefGoogle Scholar
[7]Whittlesey, E.F., “Classification of finite 2-complexes”, Proc. Amer. Math. Soc. 9 (1958), 841–845.CrossRefGoogle Scholar