Talk:Massey product

Formal Spaces
While it is indeed true that a formal space has vanishing Massey Products, the article in its current form states the converse which is false. There are non formal spaces with vanishing Massey Products. see here: http://mathoverflow.net/questions/50933/a-non-formal-space-with-vanishing-massey-products — Preceding unsigned comment added by 172.56.7.179 (talk) 06:48, 23 May 2014 (UTC)

Associativity
I am not sure the definition of massey product makes sense in a graded algebra if the latter is not associative. I think the verification of its closedness may fail if the algebra is not assumed to be associative. Anyway I learned this material from Rudyak who is an expert (unlike myself), and he always emphasized associativity, as in "dga algebra". Katzmik (talk) 15:17, 26 October 2008 (UTC)

secondary operation
Hi R.e.b.,

I think your recent edit is too drastic. It seems to make sense to have an explanation of why Massey products are called secondary operations. Please comment. Katzmik (talk) 09:05, 28 October 2008 (UTC)
 * The cup product does not have to vanish for the Massey product to be defined. It only has to vanish on certain pairs of elements. R.e.b. (talk) 14:15, 28 October 2008 (UTC)


 * Perhaps the relation of such vanishing to the name "secondary operation" could be mentioned more explicitly. Do you have any applications in mind where this distinction is important?  It may be worth including a reference. Katzmik (talk) 17:15, 28 October 2008 (UTC)


 * P.S. I would like to mention the following additional point. In order for something to be called an operation (in this case a binary one), it should be applicable to any pair of elements rather than constructing specific combinations of certain elements.  Here too I would like to reiterate the question of the previous paragraph. Katzmik (talk) 17:59, 28 October 2008 (UTC)


 * The current version, unlike some of the earlier ones, give no indication whatsoever what it means to be a higher order operation, please comment. Katzmik (talk) 15:24, 30 October 2008 (UTC)

Indeterminacy subgroup
It may be helpful to define the indeterminacy subgroup more explicitly. I think defining Massey products in the framework of an arbitrary differential graded algebra may be an error, in the absence of associativity. The latter is needed to check the closedness of the triple product. Katzmik (talk) 10:44, 29 October 2008 (UTC)
 * You might find it useful to look up the definition of Massey product and DG algebra in a standard reference, such as McCleary's book. In particular, algebras are normally understood to be associative unless they are explicitly stated not to be. This book will also answer most of your other questions. R.e.b. (talk) 15:54, 30 October 2008 (UTC)

comparison of massey products
Another topic that may be of interest is the relation between different Massey product theories, such as singular cochain and differential form. There are natural maps between them constructed using suitable quasiisomorphisms. Katzmik (talk) 11:08, 29 October 2008 (UTC)