---
OA_place: repository
OA_type: green
_id: '22171'
abstract:
- lang: eng
  text: 'We show that over the binary field [Formula: see text], the Bar-Natan perturbation
    of Khovanov homology splits as the direct sum of its two reduced theories, which
    we also prove are isomorphic. This extends Shumakovitch’s analogous result for
    ordinary Khovanov homology, without the perturbation. '
article_number: '1650014'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Yuval
  full_name: Wigderson, Yuval
  id: 2d0023a0-1567-11f0-833d-d5c1e476d4b5
  last_name: Wigderson
citation:
  ama: Wigderson Y. The Bar-Natan theory splits. <i>Journal of Knot Theory and Its
    Ramifications</i>. 2016;25(04). doi:<a href="https://doi.org/10.1142/s0218216516500140">10.1142/s0218216516500140</a>
  apa: Wigderson, Y. (2016). The Bar-Natan theory splits. <i>Journal of Knot Theory
    and Its Ramifications</i>. World Scientific Publishing. <a href="https://doi.org/10.1142/s0218216516500140">https://doi.org/10.1142/s0218216516500140</a>
  chicago: Wigderson, Yuval. “The Bar-Natan Theory Splits.” <i>Journal of Knot Theory
    and Its Ramifications</i>. World Scientific Publishing, 2016. <a href="https://doi.org/10.1142/s0218216516500140">https://doi.org/10.1142/s0218216516500140</a>.
  ieee: Y. Wigderson, “The Bar-Natan theory splits,” <i>Journal of Knot Theory and
    Its Ramifications</i>, vol. 25, no. 04. World Scientific Publishing, 2016.
  ista: Wigderson Y. 2016. The Bar-Natan theory splits. Journal of Knot Theory and
    Its Ramifications. 25(04), 1650014.
  mla: Wigderson, Yuval. “The Bar-Natan Theory Splits.” <i>Journal of Knot Theory
    and Its Ramifications</i>, vol. 25, no. 04, 1650014, World Scientific Publishing,
    2016, doi:<a href="https://doi.org/10.1142/s0218216516500140">10.1142/s0218216516500140</a>.
  short: Y. Wigderson, Journal of Knot Theory and Its Ramifications 25 (2016).
date_created: 2026-06-29T10:56:23Z
date_published: 2016-04-01T00:00:00Z
date_updated: 2026-07-14T08:48:58Z
day: '01'
doi: 10.1142/s0218216516500140
extern: '1'
external_id:
  arxiv:
  - '1508.05982'
intvolume: '        25'
issue: '04'
keyword:
- Khovanov homology
- categorification
- Bar-Natan theory
- link homology
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://doi.org/10.48550/arXiv.1508.05982
mathsc:
- 57M25
- 57M27
month: '04'
oa: 1
oa_version: Preprint
publication: Journal of Knot Theory and Its Ramifications
publication_identifier:
  eissn:
  - 1793-6527
  issn:
  - 0218-2165
publication_status: published
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Bar-Natan theory splits
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 25
year: '2016'
...