Geodesic
Topologically isotopic and smoothly inequivalent 2–spheres in simply connected 4–manifolds whose complement has a prescribed fundamental group
Torres, Rafael1
1 Scuola Internazionale Superiori di Studi Avanzati (SISSA), Trieste, Italy
Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2351-2365

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

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.

DOI : 10.2140/agt.2024.24.2351
Keywords: knotted surfaces, 4–manifolds

Torres, Rafael 1

1 Scuola Internazionale Superiori di Studi Avanzati (SISSA), Trieste, Italy 
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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. Algebraic and Geometric Topology, Tome 24 (2024) no. 4, pp. 2351-2365. doi: 10.2140/agt.2024.24.2351

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