English

Existence results of totally real immersions and embeddings into $\mathbb{C}^N$

Complex Variables 2018-05-29 v2

Abstract

We prove that the existence of totally real immersions of manifolds is a closed property under cut-and-paste constructions along submanifolds including connected sums. We study the existence of totally real embeddings for simply connected 5-manifolds and orientable 6-manifolds and determine the diffeomorphism and homotopy types. We show that the fundamental group is not an obstruction for the existence of a totally real embedding for high-dimensional manifolds in contrast with the situation in dimension four.

Keywords

Cite

@article{arxiv.1609.01062,
  title  = {Existence results of totally real immersions and embeddings into $\mathbb{C}^N$},
  author = {Marko Slapar and Rafael Torres},
  journal= {arXiv preprint arXiv:1609.01062},
  year   = {2018}
}