Montesinos Amilibia, José María and González Acuña, Francisco Javier (1980) Nonamphicheiral codimension 2 knots. Canadian Journal of Mathematics-Journal Canadien de Mathématiques, 32 (1). pp. 185-194. ISSN 0008-414X
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Official URL: http://cms.math.ca/10.4153/CJM-1980-014-x
An n-knot (Sn+2,Sn) is said to be amphicheiral if there is an orientation-reversing autohomeomorphism of Sn+2 which leaves Sn invariant as a set. An n-knot is said to be invertible if there is an orientation-preserving autohomeomorphism of Sn+2 whose restriction to Sn is an orientation-reversing autohomeomorphism of Sn. The authors prove that for any integer n there are smooth n-knots which are neither amphicheiral nor invertible. Actually, they prove it for n≥2, referring to the paper of H. F. Trotter [Topology 2 (1963), 275–280; errata, MR 30, p. 1205] for the case n=1.
The methods employed are mainly algebraic, involving for example the duality pairings of R. C. Blanchfield and J. Levine, and in most cases the work of previous authors is used to guarantee the existence of knots with the desired algebraic properties.
|Uncontrolled Keywords:||knots of codimension which are neither amphicheiral nor invertible; non- symmetric Alexander polynomial; knot cobordism group; fibred knot|
|Subjects:||Sciences > Mathematics > Topology|
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|Deposited On:||29 Nov 2012 09:43|
|Last Modified:||29 Nov 2012 09:43|
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