Topologically flat embedded 2-spheres in specific simply connected 4-manifolds

@article{Kasprowski2021TopologicallyFE,
  title={Topologically flat embedded 2-spheres in specific simply connected 4-manifolds},
  author={Daniel Kasprowski and Peter Lambert-Cole and Markus Land and Ana G. Lecuona},
  journal={2019-20 MATRIX Annals},
  year={2021}
}
In this note we study whether specific elements in the second homology of specific simply connected closed $4$-manifolds can be represented by smooth or topologically flat embedded spheres. 
Embedding surfaces in 4-manifolds
We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire–Milnor

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