i got philip hackney to try to fill me in on the last couple of meetings of the rational homotopy theory seminar that i missed...

he told me an interesting sufficient condition for a rational space to be "formal" (in a certain hopefully obvious sense...??...), that its cohomology be concentrated in even degree and be a "complete intersection" graded commutative algebra (or something like that...) ...

i don't have a good feeling yet for what this "complete intersection" condition means, "geometrically" or otherwise...

but one thing that seems interesting here already is that (if i didn't misunderstand what he was trying to tell me...) this is a condition on the cohomology... not sure yet what to make of the idea of a formalness condition expressed in terms of the cohomology alone ... ???....