ers ions . ▁The ▁quadratic ▁enh ancement ▁ ▁cru cially ▁provides ▁more ▁information ▁than ▁ ▁: ▁it ▁is ▁possible ▁to ▁kill ▁x ▁by ▁surg ery ▁if ▁and ▁only ▁if ▁. ▁The ▁corresponding ▁Ker va ire ▁invariant ▁detect s ▁the ▁surg ery ▁obst ruction ▁of ▁ ▁in ▁the ▁L - group ▁. ▁ ▁See ▁also ▁ ▁de ▁R ham ▁invariant , ▁a ▁mod ▁ 2 ▁invariant ▁of ▁- dimensional ▁manif olds ▁ ▁Notes ▁ ▁References ▁ ▁See ▁L ick or ish ▁( 1 9 9 7 ) ▁for ▁the ▁relation ▁between ▁the ▁Ar f ▁invariant ▁and ▁the ▁Jones ▁polynomial . ▁ ▁See ▁Chapter ▁ 3 ▁of ▁Carter ' s ▁book ▁for ▁another ▁equivalent ▁definition ▁of ▁the ▁Ar f ▁invariant ▁in ▁terms ▁of ▁self - inter sections ▁of ▁disc s ▁in ▁ 4 - dimensional ▁space . ▁ ▁Glen ▁B red on : ▁Top ology ▁and ▁Ge ometry , ▁ 1 9 9 3 , ▁. ▁▁ ▁J . ▁Scott ▁Carter : ▁How ▁Sur faces ▁Inter sect ▁in ▁Space , ▁Series ▁on ▁K not s ▁and ▁Everything , ▁ 1 9 9 3 , ▁. ▁▁▁▁▁ ▁W . ▁B . ▁Raymond ▁L ick or ish , ▁An ▁Introduction ▁to ▁K not ▁Theory , ▁Gr adu ate ▁Text s ▁in ▁Mathemat ics , ▁Springer , ▁ 1 9 9 7 , ▁▁▁▁ ▁Lev ▁Pon try agin , ▁Sm ooth ▁manif olds ▁and ▁their ▁applications ▁in ▁hom ot opy ▁theory ▁American ▁Mathemat ical ▁Society ▁Trans l ations , ▁Ser . ▁ 2 , ▁Vol . ▁ 1