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

Slapar, Marko; Torres, Rafael

doi:10.1090/proc/14234

Existence results of totally real immersions and embeddings into $\mathbb {C}^N$
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by Marko Slapar and Rafael Torres PDF

Proc. Amer. Math. Soc. 146 (2018), 5463-5473 Request permission

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.

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