by some homotopy class . Constructing a surjection For a locally finite collection of elements in generating it as an abelian group, the associated map induces a surjection on cohomology, meaning if we evaluate these spectra on some topological space , there is always a surjectionof Abelian groups. Steenrod-module structure on cohomology of spectra For a spectrum taking the wedge constructs a spectrum which is homotopy equivalent to a generalized Eilenberg–Maclane space with one wedge summand for each generator or . In particular, it gives the structure of a module over the Steenrod algebra for . This is because the equivalence stated before can be read asand the map induces the -structure. See also Adams spectral sequence Spectrum (topology) Homotopy groups of spheres References External links Complex cobordism and stable homotopy groups of spheres The Adams Spectral Sequence Algebraic topology Homological algebra Topology