2015/06/25 by Ali M. Elgindi, Elgindi, Ali M.
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #math.CV #math.GT
paper · pdf · doi:10.48550/arxiv.1506.07790
Complex Tangents for 3-manifolds in C3, particularly the 3-sphere
arxiv created 2015/06/25 · openalex publication_date 2015/06/25 · arxiv updated 2015/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this article, we demonstrate methods for the local removal and modification of complex tangents to embeddings of S3 into ℂ3. In particular, given any embedding of S3 and a neighborhood of the complex tangents of the embedding, we show that there exists a (C0-close) totally real embedding which agrees with the original embedding outside the given neighborhood of the complex tangents. We also demonstrate that given any knot type K in S3, either there exists an embedding of S3 which assumes non-degenerate complex tangents exactly along K or there exists a non-degenerate embedding complex tangent along two unlinked copies of K (both cases may hold). We also note possible directions of future investigations.