Matthias Nagel
Smooth and topological almost concordance
Nagel, Matthias; Orson, Patrick; Park, JungHwan; Powell, Mark
Authors
Patrick Orson
JungHwan Park
Mark Powell
Abstract
We investigate the disparity between smooth and topological almost concordance of knots in general 3-manifolds Y. Almost concordance is defined by considering knots in Y modulo concordance in Y × [0, 1] and the action of the concordance group of knots in S3 that ties in local knots. We prove that the trivial free homotopy class in every 3-manifold other than the 3-sphere contains an infinite family of knots, all topologically concordant, but not smoothly almost concordant to one another. Then, in every lens space and for every free homotopy class, we find a pair of topologically concordant but not smoothly almost concordant knots. Finally, as a topological counterpoint to these results, we show that in every lens space every free homotopy class contains infinitely many topological almost concordance classes.
Citation
Nagel, M., Orson, P., Park, J., & Powell, M. (2019). Smooth and topological almost concordance. International Mathematics Research Notices, 2019(23), 7324-7355. https://doi.org/10.1093/imrn/rnx338
Journal Article Type | Article |
---|---|
Acceptance Date | Dec 29, 2017 |
Online Publication Date | Feb 5, 2018 |
Publication Date | Dec 31, 2019 |
Deposit Date | Jan 4, 2018 |
Publicly Available Date | Feb 5, 2019 |
Journal | International Mathematics Research Notices |
Print ISSN | 1073-7928 |
Electronic ISSN | 1687-0247 |
Publisher | Oxford University Press |
Peer Reviewed | Peer Reviewed |
Volume | 2019 |
Issue | 23 |
Pages | 7324-7355 |
DOI | https://doi.org/10.1093/imrn/rnx338 |
Public URL | https://durham-repository.worktribe.com/output/1341747 |
Related Public URLs | https://arxiv.org/abs/1707.01147 |
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Copyright Statement
This is a pre-copyedited, author-produced PDF of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Nagel, Matthias, Orson, Patrick, Park, JungHwan & Powell, Mark (2018). Smooth and topological almost concordance. International Mathematics Research Notices is available online at: https://doi.org/10.1093/imrn/rnx338.
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