Journal article
On concordances in 3-manifolds
- Abstract:
- We describe an action of the concordance group of knots in the three-sphere on concordances of knots in arbitrary 3-manifolds. As an application we define the notion of almost-concordance between knots. After some basic results, we prove the existence of non-trivial almost-concordance classes in all non-abelian 3-manifolds. Afterwards, we focus the attention on the case of lens spaces, and use a modified version of the Ozsvath-Szabo-Rasmussen's tau-invariant to obstruct almost-concordances and prove that each L(p,1) admits infinitely many nullhomologous non almost-concordant knots. Finally we prove an inequality involving the cobordism PL-genus of a knot and its tau-invariants.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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- Files:
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(Preview, Accepted manuscript, pdf, 1.0MB, Terms of use)
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- Publisher copy:
- 10.1112/topo.12051
Authors
- Publisher:
- Wiley
- Journal:
- Journal of Topology More from this journal
- Volume:
- 11
- Issue:
- 1
- Pages:
- 180-200
- Publication date:
- 2018-02-23
- Acceptance date:
- 2018-01-09
- DOI:
- Keywords:
- Pubs id:
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pubs:630095
- UUID:
-
uuid:6dd1357f-cafb-4b17-ae43-8b0f9236b22e
- Local pid:
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pubs:630095
- Source identifiers:
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630095
- Deposit date:
-
2017-02-24
Terms of use
- Copyright holder:
- London Mathematical Society
- Copyright date:
- 2018
- Notes:
- © 2018 London Mathematical Society. This is the accepted manuscript version of the article. The final version is available online from Wiley at: https://doi.org/10.1112/topo.12051
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