Instantons and Bar-Natan homology

Abstract

<jats:p>A spectral sequence is established whose <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0010437X2000768X_inline1.png" /><jats:tex-math>$E_{2}$</jats:tex-math></jats:alternatives></jats:inline-formula> page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral sequence whose <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0010437X2000768X_inline2.png" /><jats:tex-math>$E_{2}$</jats:tex-math></jats:alternatives></jats:inline-formula> page is a characteristic-2 version of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0010437X2000768X_inline3.png" /><jats:tex-math>$F_{5}$</jats:tex-math></jats:alternatives></jats:inline-formula> homology in Khovanov's classification.</jats:p>