Journal article
The efficient certification of knottedness and Thurston norm
- Abstract:
- We show that the problem of determining whether a knot in the 3-sphere is non-trivial lies in NP. This is a consequence of the following more general result. The problem of determining whether the Thurston norm of a second homology class in a compact orientable irreducible 3-manifold with (possibly empty) toroidal boundary is equal to a given integer is in NP. As a corollary, the problem of determining the genus of a knot in the 3-sphere is in NP.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
Actions
Access Document
- Files:
-
-
(Preview, Accepted manuscript, 1.2MB, Terms of use)
-
- Publisher copy:
- 10.1016/j.aim.2021.107796
Authors
- Publisher:
- Elsevier
- Journal:
- Advances in Mathematics More from this journal
- Volume:
- 387
- Article number:
- 107796
- Publication date:
- 2021-06-15
- Acceptance date:
- 2021-04-07
- DOI:
- ISSN:
-
0001-8708
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:614586
- UUID:
-
uuid:0f5ec7ce-19de-4d2a-882a-64dbd08c8101
- Local pid:
-
pubs:614586
- Source identifiers:
-
614586
- Deposit date:
-
2016-04-25
Terms of use
- Copyright holder:
- Marc Lackenby
- Copyright date:
- 2021
- Rights statement:
- © 2021 Published by Elsevier Inc.
- Notes:
- This is the accepted manuscript version of the article. The final version is available online from Elsevier at https://doi.org/10.1016/j.aim.2021.107796
If you are the owner of this record, you can report an update to it here: Report update to this record