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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 an...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1112/topo.12051

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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:
pubs:630095
UUID:
uuid:6dd1357f-cafb-4b17-ae43-8b0f9236b22e
Local pid:
pubs:630095
Source identifiers:
630095
Deposit date:
2017-02-24

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