Double branched covers of 2-knots and $CP^2$

In 2023 Miyazawa produced a family of potentially exotic complex projective planes (i.e. 4-manifolds which were known to be homeomorphic to $CP^2$, but not necessarily diffeomorphic to it). These manifolds were constructed as the double branched coverings of a certain family of surface knots obtained via twisting and roll-spinning classical knots. In this talk I will show how the branched coverings of these knots can instead be obtained via torus surgeries, which can in turn be used to show that the resulting manifolds are indeed diffeomorphic to $CP^2$. This is joint work with Seungwon Kim and Maggie Miller.