JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.1. Introduction. This paper is a sequal to "Homotopy Associativity of Hspaces. I" [28], hereafter referred to as HAH I, in that it continues the study of the associative law from the point of view of homotopy theory, but knowledge of HAH I is assumed only in a few places. The essence of most of the results can be gathered from consideration of associative H-spaces (monoids); the remaining results are well represented by consideration of homotopy associative H-spaces.[Just remember that an A2-space is an H-space, an A2-form M2: X x X -? X is a multiplication, while an A3-space is a homotopy associative H-space and an A3-form consists of a multiplication and an associating homotopy.] I have attempted to make the various sections which require different background knowledge as independent as possible.?
describes the tilde construction, a generalization of the bar construction [18, Expose 3]. A few of the remarks assume familiarity with the bar construction, but the description of the tilde construction is self-contained. Theorems 2.3 and 2.7 involve the concepts of HAH I, but only the associative case as given in Corollary 2.8 will be needed in our applications and for this knowledge of the Dold and Lashof construction [3] or even the Milnor construction [8] is sufficient.Based on ?2, ?3 presents the Yessam operations in homology, which resemble the Massey operations in cohomology [31; 23] but are in no way dependent on them.?4 makes some slight mention of the An-spaces of HAH I, but the reader will find it sufficient to consider associative H-spaces. Following Sugawara [29], we define maps of such spaces, called An-maps, which are special kinds of H-maps; they are homotopy multiplicative in a strong sense. Making use of Sugawara's work, A,,-maps are related to maps of the Dold and Lashof construction [3].In ?5 the cohomology version of the spectral sequence in ?2 is applied to analyze
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.