New York Journal of Mathematics
Volume 21 (2015) 1283-1293


Ali M. Elgindi

Totally real perturbations and nondegenerate embeddings of S3

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Published: December 7, 2015
Keywords: Complex tangents, real submanifolds of complex space, totally real, 3-sphere
Subject: 32C09, 32V40, 32W99

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 ⊂ S3, either there exists an embedding of S3 which assumes nondegenerate complex tangents exactly along K or there exists a nondegenerate embedding complex tangent along two unlinked copies of K (both cases may hold). We also note possible directions of future investigations.


The author was supported in part by IRG grant no. 4010501011418 from Alfaisal University.

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Alfaisal University, Riyadh, Saudi Arabia