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Jul 1, 2020 at 17:21 comment added mathreader I'd like to mention that it is Proposition 7.1 in Chapter VI of Brown's book. (Many chapters of this book have section 7 and all items are numbered 7.x there.)
Apr 1, 2015 at 5:55 comment added Andy Putman @ChrisGerig: As you pointed out in your answer, there is no general theorem. But the result in my answer is a shadow of the UCT that does hold, is often useful, and is not well-documented in the expository literature.
Apr 1, 2015 at 5:51 comment added Chris Gerig This isn't a UCT, though. You're only swapping $M$-coefficients for $M^\ast$-coefficients.
Apr 1, 2015 at 4:49 vote accept user44191
Apr 1, 2015 at 6:11
Apr 1, 2015 at 4:17 comment added Andy Putman Sorry, I don't have time to type it out (and my copy of the book is at my office anyway; I just copied the reference from one of my old papers which quoted it). His book is pretty standard; I would expect that any university library would have it.
Apr 1, 2015 at 4:14 comment added user44191 I don't have immediate access to Brown's book; would you mind expanding with the proof?
Mar 31, 2015 at 22:00 history answered Andy Putman CC BY-SA 3.0