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Ioana Şuvaina
On finite symmetries of simply connected four-manifolds view print
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| Published: |
August 17, 2016
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| Keywords: |
4-manifolds, dissolve, Seiberg-Witten invariants, Bauer-Furuta invariants, Rosenberg conjecture |
| Subject: |
Primary 57R55, secondary 57R57, 53C21 |
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Abstract
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.
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| Acknowledgements
Supported in part by NSF grant DMS-1309029.
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| Author information
Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37214
ioana.suvaina@vanderbilt.edu
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