A cochain level proof of Adem relations in the mod 2 Steenrod algebra

Abstract In 1947, N.E. Steenrod defined the Squares, which are mod 2 cohomology operations, using explicit cochain formulae for cup- i products of cocycles. He later recast construction in more general homological terms, group homology and acyclic model methods, rather than formulae, to define p operations all primes . Steenrod’s student J. Adem applied point view prove fundamental relations, known as algebra generated by operations. this paper we give a proof relations at level. Specifically, given cocycle, produce whose coboundaries among compositions Squares original definition Square