Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group

Rafael Torres

doi:10.2140/agt.2024.24.2351

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arXiv · 2204.10089

Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group

Rafael Torres

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Abstract

We describe a procedure to construct infinite sets of pairwise smoothly inequivalent 2-spheres in simply connected 4-manifolds, which are topologically isotopic and whose complement has a prescribed fundamental group that satisfies some conditions. This class of groups include finite cyclic groups and the binary icosahedral group. These are the first known examples of knotting phenomena in 4-manifolds with such properties. Examples of locally flat embedded 2-spheres in non-smoothable 4-manifolds are also given.

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Rafael Torres. 2022-04-21. Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group. https://doi.org/10.2140/agt.2024.24.2351

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