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Every knot has characterising slopes

Abstract:

Let K be a knot in the 3-sphere. A slope p/q is said to be characterising for K if whenever p/q surgery on K is homeomorphic, via an orientation-preserving homeomorphism, to p/q surgery on another knot K in the 3-sphere, then K and K are isotopic. It was an old conjecture of Gordon, proved by Kronheimer, Mrowka, Ozsváth and Szabó, that every slope is characterising for the unknot. In this paper, we show that every knot K has infinitely many characterising slopes, confirming a conjecture of Ba...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1007/s00208-018-1757-x

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
St Catherine's College
Role:
Author
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Funding agency for:
Lackenby, M
Grant:
EP/R005125/1
Publisher:
Springer Berlin Heidelberg Publisher's website
Journal:
Mathematische Annalen Journal website
Volume:
374
Issue:
1-2
Pages:
429–446
Publication date:
2018-10-06
Acceptance date:
2018-07-30
DOI:
EISSN:
1432-1807
ISSN:
0025-5831
Source identifiers:
708228
Keywords:
Pubs id:
pubs:708228
UUID:
uuid:14712bef-c0b9-4c33-b46a-871ec9c466a0
Local pid:
pubs:708228
Deposit date:
2018-08-08

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