Abstract
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.
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Acknowledgements
The authors thank the MATRIX Institute for hospitality during the workshop “Topology of Manifolds: Interactions Between High and Low Dimensions” where the question how to prove Theorem 1 came up during a discussion session. Most of the work on this article was done during this workshop. The authors also thank Peter Teichner for helpful discussions in particular about the Kervaire–Milnor invariant.
The first author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy - GZ 2047/1, Projekt-ID 390685813. The third author was supported by the SFB 1085 “Higher Invariants” in Regensburg.
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Kasprowski, D., Lambert-Cole, P., Land, M., Lecuona, A.G. (2021). Topologically flat embedded 2-spheres in specific simply connected 4-manifolds. In: de Gier, J., Praeger, C.E., Tao, T. (eds) 2019-20 MATRIX Annals. MATRIX Book Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-030-62497-2_4
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