Embedding almost-complex manifolds in almost-complex Euclidean spaces

TL;DR

This paper proves that any compact almost-complex manifold of a given complex dimension can be embedded into a higher-dimensional Euclidean space with an almost-complex structure, using pseudo-holomorphic embeddings.

Contribution

It establishes a universal embedding result for compact almost-complex manifolds into almost-complex Euclidean spaces of specific dimensions.

Findings

Any compact almost-complex manifold of complex dimension m can be pseudo-holomorphically embedded in R^(6m).

The embedding preserves the almost-complex structure via a suitable almost-complex structure on the Euclidean space.

This extends the understanding of the geometric embedding properties of almost-complex manifolds.

Abstract

We show that any compact almost-complex manifold of complex dimension m can be pseudo-holomorphically embedded in R^(6m) equipped with a suitable almost-complex structure.