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Sep 12, 2016 at 7:56 vote accept C. Dubussy
Sep 10, 2016 at 9:27 comment added C. Dubussy So actually, all the proof was indeed in Bredon. As you said, what a nightmare ! Thank you very much for this complete answer, I'll read it more carefully monday at work and then I'll accept it.
Sep 10, 2016 at 5:20 history edited Greg Friedman CC BY-SA 3.0
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Sep 10, 2016 at 2:51 comment added Greg Friedman Oops, thanks for the reminder that I need to continue thinking about this. I realized that I might not have ever thought this through for spaces that aren't manifolds or pseudomanifolds, but I'll let you know if I come up with something.
Sep 8, 2016 at 19:12 comment added C. Dubussy Thanks for this answer, I'm impatient to read your further developments but these have already given interesting ideas. As you said, in the case of manifolds with orientation sheaf, things are easier and we can by the way find some books that treat this case. (At least partially.)
Sep 8, 2016 at 12:13 history answered Greg Friedman CC BY-SA 3.0