 

Ioana Şuvaina
On finite symmetries of simply connected fourmanifolds view print


Published: 
August 17, 2016

Keywords: 
4manifolds, dissolve, SeibergWitten invariants, BauerFuruta invariants, Rosenberg conjecture 
Subject: 
Primary 57R55, secondary 57R57, 53C21 


Abstract
For most positive integer pairs (a,b),
the topological space #aCP^{2}#b\overline{CP^{2}} is shown to
admit infinitely many inequivalent smooth structures
which dissolve upon performing a single connected sum
with S^{2}×S^{2}. This is then used to
construct infinitely many nonequivalent smooth free actions of suitable finite groups on the connected sum
#aCP^{2}#b\overline{CP^{2}}. 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 counterexamples to the 4dimensional Rosenberg Conjecture.


Acknowledgements
Supported in part by NSF grant DMS1309029.


Author information
Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN 37214
ioana.suvaina@vanderbilt.edu

