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May 11, 2011 at 12:23 comment added HenrikRüping maybe Ryan or David can repost this as an answer and close the question ?
May 10, 2011 at 23:03 comment added David Carchedi @Ryan: Thanks. I'm glad to see that there is such a simple counter-example.
May 10, 2011 at 18:57 comment added Ryan Budney I suspect the answer is yes for connected topological manifolds but I don't have an argument off the top of my head. These kinds of questions were investigated in the 60's as far as I know.
May 10, 2011 at 17:47 comment added Ryan Budney The answer is no. Consider your space to be a wedge of a bunch of circles -- and don't use common wedge points. Then an involution can fix a neighbourhood of a point and still flip some of the circle wedge summands.
May 10, 2011 at 17:37 history asked David Carchedi CC BY-SA 3.0