Higher Order Massey Products
More generally the n-fold Massey product 〈a1,1, a2,2, ...,an,n〉 of n elements of H(Γ) is defined to be the set of elements of the form
for all solutions of the equations
- , 1 ≤ i ≤ j ≤ n, (i,j) ≠ (1,n).
In other words it can be thought of as the obstruction to solving the latter equations for all 1≤i≤j≤n, in the sense that it contains the 0 cohomology class if and only if these equations are solvable. This n-fold Massey product is an n−1 order cohomology operation, meaning that for it to be nonempty many lower order Massey operations have to contain 0, and moreover the cohomology classes it represents all differ by terms involving lower order operations. The 2-fold Massey product is just the usual cup product and is a first order cohomology operation, and the 3-fold Massey product is the same as the triple Massey product defined above and is a secondary cohomology operation.
May (1969) described a further generalization called Matric Massey products, which can be used to describe the differentials of the Eilenberg–Moore spectral sequence.
Read more about this topic: Massey Product
Famous quotes containing the words higher, order and/or products:
“Universal empire is the prerogative of a writer. His concerns are with all mankind, and though he cannot command their obedience, he can assign them their duty. The Republic of Letters is more ancient than monarchy, and of far higher character in the world than the vassal court of Britain.”
—Thomas Paine (1737–1809)
“I had to kick their law into their teeth in order to save them.
However I have heard that sometimes you have to deal
Devilishly with drowning men in order to swim them to shore.
Or they will haul themselves and you to the trash and the fish beneath.”
—Gwendolyn Brooks (b. 1917)
“Good wine needs no bush,
And perhaps products that people really want need no
hard-sell or soft-sell TV push.
Why not?
Look at pot.”
—Ogden Nash (1902–1971)