New York Journal of Mathematics
Volume 22 (2016) 853-863


Ioana Şuvaina

On finite symmetries of simply connected four-manifolds

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Published: August 17, 2016
Keywords: 4-manifolds, dissolve, Seiberg-Witten invariants, Bauer-Furuta invariants, Rosenberg conjecture
Subject: Primary 57R55, secondary 57R57, 53C21

For most positive integer pairs (a,b), the topological space #aCP2#b\overline{CP2} is shown to admit infinitely many inequivalent smooth structures which 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#b\overline{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.


Supported in part by NSF grant DMS-1309029.

Author information

Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37214