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An obstruction to a knot being deform-spun via Alexander polynomials

Authors: Ryan Budney and Alexandra Mozgova
Journal: Proc. Amer. Math. Soc. 137 (2009), 3547-3552
MSC (2000): Primary 57R40
Published electronically: May 27, 2009
MathSciNet review: 2515425
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Abstract: We show that if a co-dimension two knot is deform-spun from a lower-dimensional co-dimension 2 knot, there are constraints on the Alexander polynomials. In particular this shows, for all $ n$, that not all co-dimension 2 knots in $ S^n$ are deform-spun from knots in $ S^{n-1}$.

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Additional Information

Ryan Budney
Affiliation: Department of Mathematics and Statistics, University of Victoria, P.O. Box 3045 STN CSC, Victoria, British Columbia, Canada V8W 3P4

Alexandra Mozgova
Affiliation: ACRI, 260 route du Pin Montard, BP 234, F-06904 Sophia Antipolis Cedex, France

Received by editor(s): November 18, 2007
Received by editor(s) in revised form: February 16, 2009
Published electronically: May 27, 2009
Additional Notes: The authors would like to thank the Max Planck Institute for Mathematics for its hospitality. The first author would also like to thank the Institut des Hautes Études Scientifiques for its hospitality, as well as Danny Ruberman and an anonymous referee for many useful comments on the paper.
Communicated by: Daniel Ruberman
Article copyright: © Copyright 2009 American Mathematical Society