Loops of H-spaces with finitely generated cohomology rings

Loop spaces of H-spaces with finitely generated cohomology

“…Our theorem also generalizes a result of Lin [12] who has shown Theorem A under the assumption that X is an A p -space in the sense of Stasheff [19]. We owe much to the results in [12] and [13] (see §2). From the result of Hemmi, it may be possible to generalize our result to the case of quasi C p -spaces instead of loop spaces on H-spaces.…”

Homotopy commutativity of $H$-spaces with finitely generated cohomology

“…Theorem B generalizes his result to the case of C p -spaces with finitely generated mod p cohomology. We see that Theorem B also generalizes results of Lin [14] and Kawamoto [13], in which the same result was proved under the assumption that X is the loop space of an H-space. This paper is organized as follows: In §2 we recall the Dror Farjoun localization functor with respect to a space introduced in [9].…”

“…In [13], we proved that if X is a simply connected mod p H-space such that H * (ΩX) is a finitely generated algebra, then ΩX is homotopy equivalent to a finite product of Eilenberg-Mac Lane spaces of dimensions 1 and 2 (see also [14]). By combining a result of Aguadé-Smith [3] with the above argument, we have a simple proof of [13, Thm.…”

“…At present, only a few results are known for such Hspaces (cf. [5], [8], [13], [14], [16], [22], [23]). Recently, Broto and Crespo [5], [8] gave an important result for H-spaces with finitely generated cohomology.…”

Higher homotopy commutativity of H-spaces and homotopy localizations

“…Corollary 1.2 is a generalization of results from [Aguadé and Smith 1986;Kawamoto 1999;Lin 1994]. Bousfield [2001] studied the K (n) * -localizations of Postnikov H -spaces, where K (n) * denotes the Morava K -homology theory for n ≥ 1.…”