**Edit:** According to comment of Michał Kukieła I revised the question


A topological space $X$ satisfies "Homeo-fixed point" property if every homeomorphism $f$ on $X$ possess a fixed point.



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> Is there an example of a connected manifold with this property but does not satisfies fixed point property?
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**Edit** Now i found a related paper, so I add the link to this question:


<http://link.springer.com/article/10.1007%2FBF02771655>



Homeo-Fixed point property
consider the connected sum of the klein bottle with the projective plane


there is a map with no fixed point
collapse to the klein bottle and rotate


any homeo induces a map on mod two homology which is an isomorphism
 respecting the intersection form


i didn't calculate but if the trace mod two of any such 3x3 matrix is non zero then
any homeomorphism has a fixed point


in any case this is an idea to construct an example


Dennis Sullivan


