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Double branched covers of knotoids

Abstract:

By using double branched covers, we prove that there is a 1-1 correspondence between the set of knotoids in S2, up to orientation reversion and rotation, and knots with a strong inversion, up to conjugacy. This correspondence allows us to study knotoids through tools and invariants coming from knot theory. In particular, concepts from geometrisation generalise to knotoids, allowing us to characterise reversibility and other properties in the hyperbolic case. Moreover, with our construction we...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.4310/CAG.2022.v30.n5.a3

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Role:
Author
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Name:
Royal Society
Grant:
UF150238
Publisher:
International Press
Journal:
Communications in Analysis and Geometry More from this journal
Volume:
30
Issue:
5
Pages:
1007–1057
Publication date:
2023-03-17
Acceptance date:
2019-10-08
DOI:
EISSN:
1944-9992
ISSN:
1019-8385
Language:
English
Keywords:
Pubs id:
1315374
Local pid:
pubs:1315374
Deposit date:
2022-12-16

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