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Non-loose negative torus knots

Abstract:

We study Legendrian and transverse realizations of the negative torus knots T(p,−q) in all contact structures on the 3-sphere. We give a complete classification of the strongly non-loose transverse realizations and the strongly non-loose Legendrian realizations with the Thurston-Bennequin invariant smaller than −pq. Additionally, we look at the Legendrian invariants of these knots in the minus version of the knot Floer homology, obtaining that U · L(L) vanishes for any Legendrian negative tor...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4171/QT/169

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-4378-1797
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Name:
European Commission
Grant:
674978
Publisher:
European Mathematical Society
Journal:
Quantum Topology More from this journal
Volume:
13
Issue:
4
Pages:
669–689
Publication date:
2023-01-27
Acceptance date:
2021-02-21
DOI:
EISSN:
1664-073X
ISSN:
1663-487X
Language:
English
Keywords:
Pubs id:
1166349
Local pid:
pubs:1166349
Deposit date:
2021-03-07

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