On finite symmetries of simply connected four-manifolds

摘要

For most positive integer pairs (a,b), the topological space #aCP2#boverline{CP2} is shown to admit infinitely many inequivalent smooth structureswhich dissolve upon performing a single connected sum with S2×S2. This is then used to construct infinitely many nonequivalent smooth free actions of suitable finite groups on the connected sum #aCP2#boverline{CP2}. We then investigate the behavior of the sign of the Yamabe invariant for the resulting finite covers, and observe that these constructions provide many new counter-examples to the 4-dimensional Rosenberg Conjecture.