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.
Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds / Torres, Rafael. - In: ANNALES DE L'INSTITUT FOURIER. - ISSN 1777-5310. - 75:6(2025), pp. 2501-2527. [10.5802/aif.3685]
Smoothly knotted and topologically unknotted nullhomologous surfaces in 4-manifolds
Torres, Rafael
2025-01-01
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.| File | Dimensione | Formato | |
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