Torsion in H-Spaces, I

Torsion in the homology of 𝐻-spaces

“…Our motivation for this approach comes from finite //-space theory. Certain cases of our restrictions or of the absence of torsion in H*(ÇLX\ Z) have been proven for finite //-spaces (see [6]) or, at least, for compact Lie groups (see [1], [3] and [7]). Our arguments tie these results together and, furthermore, show that the relations do not depend on the finiteness of the spaces involved.…”

BP torsion in finite $H$-spaces

“…This unstable relation gives rise to an unstable "secondary operation" <f> defined on ß (see [18]). Recall that n = pk + x + • • ■ +pl+x + p'"' + ••• +p + 1.…”

A conjecture on the 𝑝-regularity of an 𝐻-space

“…The author has tried unsuccessfully to find a proof of this result which does not rely upon the classification of semisimple Lie groups. Now Lin has shown in Theorem 4.1.1 of [12] that the integral homology of the space of based loops on a simply connected finite //-space has no odd torsion. This represents a major step forward in trying to establish analogues of the results of Atiyah, Hirzebruch and Hodgkin mentioned above when G is replaced by a suitable finite //-space (see Theorem 4.6.3 of [12]).…”

“…Now Lin has shown in Theorem 4.1.1 of [12] that the integral homology of the space of based loops on a simply connected finite //-space has no odd torsion. This represents a major step forward in trying to establish analogues of the results of Atiyah, Hirzebruch and Hodgkin mentioned above when G is replaced by a suitable finite //-space (see Theorem 4.6.3 of [12]). The conjecture of the title is that Theorem 1.1. remains true when G is assumed only to be finite, associative //-space.…”