Inverse Limits of Real Projective Spaces and the Fixed Point Property
by
Marcus Marsh
Cal. State Univ, Sacramento

In an earlier paper, the author “proved” that inverse limits on even-dimensional real projective spaces with essential bonding maps have the fixed point property. The “proof” given by the author in that paper does not work for one homotopy class of self maps on even-dimensional real projective spaces, namely for essential maps that induce trivial maps in the first homology group. We consider a representative “unimodal” map f from this homotopy class and the inverse limit space X obtained using f as the bonding map. The space X is a union of diadic solenoids having exactly one point in common, and it has the fixed point property.

Date received: February 23, 2006