This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism b
n(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π
F) and F
F) for other cohomology theories E
*(−) and F
*(−). These upper bounds do not depend on X and are given in terms of the exponents of the stable homotopy groups of spheres and, for the last three homomorphisms, in terms of the order of the Postnikov invariants of the spectrum F.
Open Mathematics is a fully peer-reviewed, open access, electronic journal that publishes significant and original works in all areas of mathematics. The journal publishes both research papers and comprehensive and timely survey articles. Open Math aims at presenting high-impact and relevant research on topics across the full span of mathematics.