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Torres, Rafael

Topologically isotopic and smoothly inequivalent 2-spheres in simply connected 4-manifolds whose complement has a prescribed fundamental group. (English) Zbl 07904859

Algebr. Geom. Topol. 24, No. 4, 2351-2365 (2024).
Summary: 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 cyclic groups and the binary icosahedral group. These are the first known examples of such exotic embeddings of 2-spheres in 4-manifolds. Examples of locally flat embedded 2-spheres in a nonsmoothable 4-manifold whose complements are homotopy equivalent to smoothly embedded ones are also given.

MSC:

57K45 Higher-dimensional knots and links
57R55 Differentiable structures in differential topology
57R40 Embeddings in differential topology
57R52 Isotopy in differential topology

Keywords:

knotted surfaces; 4-manifolds
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Full Text: DOI arXiv

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