A cork of the rational surface with the second Betti number 9

Abstract

We provide the first explicit example of a cork of ${\mathbf{CP}}^2\#8\overline{{\mathbf{CP}}^2}$. This result gives the current smallest second Betti number of a standard simply-connected closed $4$-manifold for which an explicit cork has been found.

24 pages, 31 figures. v3 includes many improvements in the exposition and corrections to Figures 5, 7, 8, 9, 10, 13, thanks to the anonymous referee. This version agrees with the published version

References in corpus (3)

• Corks, Plugs and exotic structures
• Exotic Smooth Structures on Small 4-Manifolds
• Isotopy of the Dehn twist on K3#K3 after a single stabilization