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The generalized Boardman homomorphisms

100%

Arlettaz D.

Open Mathematics

2004

tom 2

nr 1

50-56

This paper provides universal upper bounds for the exponent of the kernel and of the cokernel of the classical Boardman homomorphism b n: π n(X)→H n(H;ℤ), from the cohomotopy groups to the ordinary integral cohomology groups of a spectrum X, and of its various generalizations π n(X)→E n(X), F n(X)→(E∧F)n(X), F n(X)→H n(X;π 0 F) and F n(X)→H n+t(X;π t 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.

Postnikov invariants of H-spaces

63%

Arlettaz D., Pointet-Tischler N.

Fundamenta Mathematicae

1999

tom 161

nr 1-2

17-35

It is known that the order of all Postnikov k-invariants of an H-space of finite type is finite. This paper establishes the finiteness of the order of the k-invariants $k^{m+1}(X)$ of X in dimensions m ≤ 2n if X is an (n-1)-connected H-space which is not necessarily of finite type (n ≥ 1). Similar results hold more generally for higher k-invariants if X is an iterated loop space. Moreover, we provide in all cases explicit universal upper bounds for the order of the k-invariants of X.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Open Mathematics

2 Arlettaz D.

1 Pointet-Tischler N.

1 2004

1 1999

Wyniki wyszukiwania

The generalized Boardman homomorphisms

Postnikov invariants of H-spaces