Published online by Cambridge University Press: 10 July 2020
Building upon our earlier work with M. C. Hughes, we construct many new smooth structures on closed simply connected nonspin
$4$
-manifolds with positive signature. We also provide numerical and asymptotic upper bounds on the function
$\lambda (\sigma )$
that was defined in our earlier work.
The first author was partially supported by a Simons Research Fellowship and Collaboration Grant for Mathematicians from the Simons Foundation. The second author was partially supported by an NSERC discovery grant.