Joe, Aha! Speaking to you suggested a revised and much more reasonable condition on A \int B \int (∂M x ∂N) than the one we spoke about: that it must be empty. Checking the new one out now. If the proof works that way, then we're probably OK. I thought about Berkeley, and we might or might not be able to make it. But meanwhile, I look forward to the next time we can talk about math unhurriedly in person. —Dan