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Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds

Torres, Rafael
2025
  • journal article

Periodico
ANNALES DE L'INSTITUT FOURIER
Abstract
We point out that recent constructions of inequivalent smooth structures yield a manufacturing procedure of infinite sets of topologically isotopic and pairwise smoothly inequivalent nullhomologous 2-spheres and 2-tori inside a myriad of 4-manifolds. These surfaces bound a locally flat embedded handlebody but not a smoothly embedded one, and include the first examples of nullhomotopic 2-spheres in closed 4-manifolds to display such behavior. We exhibit an example of a locally flat non-smoothable embedding of a nullhomotopic 2-sphere in a closed smooth simply connected 4-manifold.
DOI
10.5802/aif.3685
WOS
WOS:001597330500007
Archivio
https://hdl.handle.net/20.500.11767/150291
info:eu-repo/semantics/altIdentifier/scopus/2-s2.0-105014346187
https://aif.centre-mersenne.org/articles/10.5802/aif.3685/
Diritti
open access
license:creative commons
license uri:http://creativecommons.org/licenses/by-nd/4.0/
Soggetti
  • surfaces, 4-manifolds...

  • Settore MAT/03 - Geom...

  • Settore MATH-02/B - G...

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