Gespeichert in:
| 1. Verfasser: | |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2603.07785 |
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Inhaltsangabe:
- Let f, g be two homotopic smooth embeddings of a closed surface in a closed oriented 5-dimensional manifold. We show that if f admits a common algebraic dual 3-sphere, or if the fundamental group of the ambient space is trivial, then f and g must be isotopic. This generalizes a result of Kosanovic, Schneiderman, and Teichner. The proof is based on the construction of an invariant that classifies the isotopy classes of smooth embeddings of surfaces in ambient 5-dimensional manifolds within a homotopy class, which may be of independent interest. The invariant is defined in terms of the homotopy groups of the 5-dimensional manifold.