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Apr 16, 2011 at 23:43 vote accept Sergey Melikhov
Apr 12, 2011 at 17:40 answer added Sergey Melikhov timeline score: 2
Apr 4, 2011 at 9:05 history edited Sergey Melikhov CC BY-SA 2.5
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Apr 4, 2011 at 2:45 answer added Qayum Khan timeline score: 1
Apr 4, 2011 at 1:57 comment added Sergey Melikhov Of course, the nontrivial case is when they are not preserved, and this was the point of the example. Sorry if it doesn't read smoothly.
Apr 4, 2011 at 1:10 comment added Tom Goodwillie In the example you mention, $N$ and its complement are interchanged by the involution. This is not clear from your first paragraph; at first I imagined that $P$ and $N$ were subpolyhedra of $M$ preserved by the involution (in which the question could be approached by working in the orbit space).
Apr 4, 2011 at 0:16 history asked Sergey Melikhov CC BY-SA 2.5