article published yes Yuval Wigderson author 2d0023a0-1567-11f0-833d-d5c1e476d4b5 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. World Scientific Publishing2016 eng Khovanov homologycategorificationBar-Natan theorylink homology 0218-2165 1793-6527 1508.0598210.1142/s0218216516500140 2504 yes 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>. 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> 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>. Y. Wigderson, “The Bar-Natan theory splits,” <i>Journal of Knot Theory and Its Ramifications</i>, vol. 25, no. 04. World Scientific Publishing, 2016. Wigderson Y. 2016. The Bar-Natan theory splits. Journal of Knot Theory and Its Ramifications. 25(04), 1650014. 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> Y. Wigderson, Journal of Knot Theory and Its Ramifications 25 (2016). 221712026-06-29T10:56:23Z2026-07-14T08:48:58Z