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KNOTTED 2-SPHERES IN TUBES IN Z⁴

C. E. SOTEROS

Department of Mathematics and Statistics, University of Saskatchewan, Saskatoon, SK S7N 5E6, Canada

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D. W. SUMNERS

Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA

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, and

S. G. WHITTINGTON

Department of Chemistry, University of Toronto, Toronto, ON M5S 3H6, Canada

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https://doi.org/10.1142/S0218216512501167Cited by:5 (Source: Crossref)

Abstract

We prove a pattern theorem for 2-spheres in tubes in Z⁴ and use this to prove that all except exponentially few 2-spheres in a tube in Z⁴ are knotted. We sketch how the argument can be applied to prove the same result for p-spheres in a tube in Z^p+2, p > 2.

Keywords:

AMSC: 57Q45, 05A16, 82B41

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