Mark Hughes (BYU) - Branched covers of twist roll spun 2-knots and CP^2

Speaker: Mark Hughes

Abstract: 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 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}.  We also use these results to show that certain homotopy 4-spheres created by Juhász-Powell are also standard. This is joint work with Seungwon Kim and Maggie Miller.