From: "Samson Saneblidze" Date: Wed, 2 Aug 2006 21:02:26 +0400 >> Subject: Massey products >> From: Mark Grant >> Date: Tue, 1 Aug 2006 17:58:50 +0100 (BST) >> >> Hi everyone, >> does anyone know about the behaviour of Massey triple products (with >> field coefficients) with respect to external products? I had hoped for >> something simple like >> >> < a\otimes b,c\otimes d,e\otimes f>\subseteq\otimes >> >> (apologies for the tex speak) but it seems this is either false or >> tricky to prove (involving Eilenberg-Zilber maps and wotnot). A correct fact on a behavior of Massey products with respect to the tensor products is the following: If both Massey triple products < a ,c, e > and < b, d, f > are defined, then the Massey triple product < a \otimes b, c \otimes d, e \otimes f > is defined and contains zero . Note that the analogous statement is valid for Massey products of any order as well. For example, such a behavior of Massey products on tensor products can be immediately deduced by combining the following two facts: 1. the relationship between Massey products and A(infty)-algebra operations on the homology of any dg algebra; 2. the explicit formula expressing the A(infty)-algebra operations on the tensor product by the operations on tensor factors (for the second item, see "S. Saneblidze and R. Umble, Diagonals on the permutahedra, multiplihedra and associahedra, Homotopy, Homology and Appl., 6(1), (2004), 363-411, math. AT/0209109 "). Samson Saneblidze