algebra ▁. ▁▁ ▁The ▁Alexander ▁polynomial ▁ ▁is ▁the ▁E uler ▁characteristic ▁of ▁a ▁big rad ed ▁kn ot ▁hom ology ▁theory . ▁ ▁is ▁trivial . ▁The ▁Jones ▁polynomial ▁ ▁is ▁the ▁E uler ▁characteristic ▁of ▁a ▁big rad ed ▁link ▁hom ology ▁theory . ▁The ▁entire ▁H OM FL Y - PT ▁polynomial ▁is ▁the ▁E uler ▁characteristic ▁of ▁a ▁trip ly ▁grad ed ▁link ▁hom ology ▁theory . ▁ ▁App lications ▁The ▁first ▁application ▁of ▁Kh ovan ov ▁hom ology ▁was ▁provided ▁by ▁Jacob ▁R asm ussen , ▁who ▁defined ▁the ▁s - in variant ▁using ▁Kh ovan ov ▁hom ology . ▁This ▁integer ▁val ued ▁invariant ▁of ▁a ▁kn ot ▁gives ▁a ▁bound ▁on ▁the ▁slice ▁genus , ▁and ▁is ▁sufficient ▁to ▁prove ▁the ▁Mil nor ▁conject ure . ▁ ▁In ▁ 2 0 1 0 , ▁K ron heimer ▁and ▁M row ka ▁proved ▁that ▁the ▁Kh ovan ov ▁hom ology ▁detect s ▁the ▁un k not . ▁The ▁categor ified ▁theory ▁has ▁more ▁information ▁than ▁the ▁non - c ategor ified ▁theory . ▁Although ▁the ▁Kh ovan ov ▁hom ology ▁detect s ▁the ▁un k not , ▁it ▁is ▁not ▁yet ▁known ▁if ▁the ▁Jones ▁polynomial ▁does . ▁ ▁Notes ▁ ▁References ▁. ▁. ▁. ▁. ▁. ▁. ▁. ▁ ▁External ▁links ▁Kh ovan ov ▁hom ology ▁is ▁an ▁un k not - det ector ▁by ▁K ron heimer ▁and ▁M row ka ▁▁ ▁Hand - written ▁sl ides ▁of ▁M . ▁Kh ovan ov ' s