Intersection homology operations (Q799976)

This paper gives a sheaf-theoretic construction of Steenrod squares in (mod 2) intersection (co-)homology, which double the perversity. If X is a (mod 2) Witt space, then by Poincaré duality the Steenrod squares give rise to ''intersection homology Wu classes'', \(IV_*(X)\in IH_*^{\bar m}(X)\) in the middle intersection homology groups. The total square of this class is an ''intersection homology Whitney class''. \(IW_*(X)=S_ qIV_*(X)\in H_*(X)\) whose associated genus, \(IW_ 0(X)\) is the (mod 2)-intersection homology Euler characteristic. A combinatorial formula for these characteristic classes is given.