Building upon our earlier work with M. C. Hughes, we construct many new smooth structures on closed simply connected nonspin -manifolds with positive signature. We also provide numerical and asymptotic upper bounds on the function that was defined in our earlier work.
Bibliographical noteFunding Information:
Received by the editors May 9, 2020. Published online on Cambridge Core July 10, 2020. e first author was partially supported by a Simons Research Fellowship and Collaboration Grant for Mathematicians from the Simons Foundation. e second author was partially supported by an NSERC discovery grant. AMS subject classification: 57K43, 57R55. Keywords: Symplectic 4-manifold, geography, knot surgery, symplectic normal sum.