Generic immersions and totally real embeddings
Geometric Topology
2019-09-27 v4 Complex Variables
Differential Geometry
Abstract
We show that, for a closed orientable n-manifold, with n not congruent to 3 modulo 4, the existence of a CR-regular embedding into complex (n-1)-space ensures the existence of a totally real embedding into complex n-space. This implies that a closed orientable (4k+1)-manifold with non-vanishing Kervaire semi-characteristic possesses no CR-regular embedding into complex 4k-space. We also pay special attention to the cases of CR-regular embeddings of spheres and of simply-connected 5-manifolds.
Cite
@article{arxiv.1803.08238,
title = {Generic immersions and totally real embeddings},
author = {Naohiko Kasuya and Masamichi Takase},
journal= {arXiv preprint arXiv:1803.08238},
year = {2019}
}
Comments
9 pages; the title has been changed; a mistake in Theorem 5.4 (c) has been corrected