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January 17, 2026Proceedings of the American Mathematical Society0 citations

Exotically knotted 2-spheres and the fundamental groups of their complements

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YBYounes Benyahia

Key Points

  • This work explores the relationship between finitely presented groups and 2-links in closed 4-manifolds.
  • Construct a closed simply connected 4-manifold containing an infinite family of 2-links.
  • Demonstrate topological isotopy and smooth inequivalence among these 2-links.
  • Examine the conditions under which the 2-link group equals the specified finitely presented group.
  • Identified a family of topologically isotopic but smoothly inequivalent 2-links for any given finitely presented group.
  • Established that under specific topological conditions, the components of these 2-links are nullhomotopic.

Abstract

We show that for any finitely presented group G G , there is a simply connected closed 4-manifold containing an infinite family of topologically isotopic but smoothly inequivalent 2-links whose 2-link group is G G . We also show that, if G G satisfies the necessary topological conditions, these 2-links have nullhomotopic components.

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Cite This Study

Younes Benyahia (2026) studied this question.

synapsesocial.com/papers/696b25a9d2a12237a9348fe7https://doi.org/10.1090/proc/17517
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