Simple non-finite knots are not prime in higher dimensions

Kearton, C.; Wilson, S.M.J.

Abstract

It has long been known that in high dimensions tbere are examples of irreducible knots which are not prime. Here we show that in fact there are no prime simple knots in high dimensions, with the possible exception of those whose homology is finite. In particular, the result holds for all simple (2q - 1)-knots, q > 1.

Citation

Kearton, C., & Wilson, S. (2003). Simple non-finite knots are not prime in higher dimensions. Journal of Knot Theory and Its Ramifications, 12(02), 225-241. https://doi.org/10.1142/s0218216503002408

• Journal Article Type: Article
• Publication Date: Mar 1, 2003
• Deposit Date: Feb 15, 2008
• Journal: Journal of Knot Theory and Its Ramifications
• Print ISSN: 0218-2165
• Electronic ISSN: 1793-6527
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Issue: 02
• Pages: 225-241
• DOI: https://doi.org/10.1142/s0218216503002408