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A stub Massey product and a longer Toda bracket (still plenty gaps of reference, many many unlinked words). No promises w.r.t. spellings.
I now see I’ve missed the convention for capitalization. Will fix that now… done.
Cheers
Thanks!!
I did some editing, as usual: added hyperlinks, a table of contents, a Referemces-section, pointers to the References, etc.
Notice that top-level sections need two hash-signs to appear in the TOC correctly:
## Idea
## Definition
### General
### Some special case
CoThanks, too. also, the definition now makes sense.
OK, maybe I’ll take this next question to MO, but:
the Toda Bracket should directly give something like the Massey Product, because if you have a bunch of maps $u_i : X \to K_i$ where the $K_i$ are suitable Eilenberg-Mac Lane spaces, one has a sequence of maps of pointed-function spaces
$K_1^X \to (K_1 \otimes K_2)^X \cdots \to (K_1\otimes \cdots K_{n+2})^X$representing the particular cup products $\bullet\smallsmile u_i$, as well as a map
$\mathbb{S}^0 \to K_1^X$adjoint to $u_1$. Then the bracket machinery highlights a family of maps
$\mathbb{S}^{n} \to (K_1 \otimes \cdots K_{n+2})^X$adjoint to
$\Sigma^n X \to K_1 \otimes \cdots \otimes K_{n+2} .$It seems intuitive to me (don’t ask why) that the construction of Massey products should at least give a subset of these Toda brackets, but I don’t feel so clear about the vice-versa. Does anyone know if this is at least spelled-out somewhere? (McCleary’s book on SpSeqs, e.g., is perfectly vague about these brackets, at least in a neighborhood of index entries.)
Added references
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