Integral cohomology of 2-local Hopf spaces with at most two non-trivial finite homotopy groups. (English) Zbl 1096.57021
Arlettaz, Dominique (ed.) et al., An alpine anthology of homotopy theory. Proceedings of the 2nd Arolla conference on algebraic topology, Arolla, Switzerland, August 24–29, 2004. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3696-X/pbk). Contemporary Mathematics 399, 87-99 (2006).
Let \(X\) be a connected topological space having the homotopy type of a CW-complex. If there is an integer \(h\geq 1\) such that \(h.\widetilde{H}^*(X;{\mathbb Z})=0\), then one says that \(X\) admits a homology exponent. In the paper under review, the author proves that a non-contractible simply-connected 2-local \(H\)-space, with at most two non-trivial finite homotopy groups, has no homology exponent. The paper ends with a list of questions and conjectures connected to the main result.
For the entire collection see [Zbl 1086.55001].
For the entire collection see [Zbl 1086.55001].
Reviewer: Daniel Tanré (Villeneuve d’ Ascq)
