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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.07785 |
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Table of Contents:
- 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.