{"publication_status":"published","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1508.05982","open_access":"1"}],"doi":"10.1142/s0218216516500140","_id":"22171","oa_version":"Preprint","day":"01","language":[{"iso":"eng"}],"OA_place":"repository","OA_type":"green","abstract":[{"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. ","lang":"eng"}],"oa":1,"title":"The Bar-Natan theory splits","status":"public","date_created":"2026-06-29T10:56:23Z","issue":"04","article_type":"original","article_processing_charge":"No","article_number":"1650014","extern":"1","month":"04","quality_controlled":"1","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","keyword":["Khovanov homology","categorification","Bar-Natan theory","link homology"],"scopus_import":"1","external_id":{"arxiv":["1508.05982"]},"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>","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>.","ista":"Wigderson Y. 2016. The Bar-Natan theory splits. Journal of Knot Theory and Its Ramifications. 25(04), 1650014.","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.","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>.","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>","short":"Y. Wigderson, Journal of Knot Theory and Its Ramifications 25 (2016)."},"date_updated":"2026-07-14T08:48:58Z","year":"2016","type":"journal_article","arxiv":1,"publisher":"World Scientific Publishing","mathsc":["57M25","57M27"],"publication":"Journal of Knot Theory and Its Ramifications","publication_identifier":{"eissn":["1793-6527"],"issn":["0218-2165"]},"author":[{"last_name":"Wigderson","full_name":"Wigderson, Yuval","first_name":"Yuval","id":"2d0023a0-1567-11f0-833d-d5c1e476d4b5"}],"intvolume":"        25","volume":25,"date_published":"2016-04-01T00:00:00Z"}