On embeddings of almost complex manifolds in almost complex Euclidean spaces

Abstract

We prove that any compact almost complex manifold $(M,J)$ of real dimension $2m$ admits a pseudo-holomorphic embedding in a Euclidean space of dimension $4m+2$, endowed with a suitable non-standard almost complex structure. Moreover, we give a necessary and sufficient condition, expressed in terms of the Segre class of $(M,J)$, for the existence of an embedding or an immersion in an almost complex Euclidean $4m$-space. We also discuss the pseudo-holomorphic embeddings of an almost complex 4-manifold in $R^6$.

11 pages; minor revision to match the published version

References in corpus (1)

• Embedding almost-complex manifolds in almost-complex Euclidean spaces

Cited by in corpus (2)

• Generic immersions and totally real embeddings
• Universal Lefschetz fibrations and Lefschetz cobordisms