On embeddings of 4-manifolds in codimension 2

Ghanwat, Abhijeet; Pancholi, Dishant M

doi:10.2140/agt.2026.26.1293

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On embeddings of $4$-manifolds in codimension $2$

Abhijeet Ghanwat and Dishant M Pancholi

Algebraic & Geometric Topology 26 (2026) 1293–1320

DOI: 10.2140/agt.2026.26.1293

Abstract

We show that every closed orientable smooth $4$ -manifold admits a smooth embedding in a large class of closed $6$ -manifolds. In particular, we show that every smooth $4$ -manifold admits a smooth embedding in the complex projective $3$ -space. Our embedding technique also provides a new proof of embeddings of $4$ -manifolds in $ℝ^{7}$ .

Keywords

embeddings, manifolds, cell complexes

Mathematical Subject Classification

Primary: 57R40

References

Publication

Received: 13 June 2021

Revised: 14 April 2025

Accepted: 5 May 2025

Published: 25 April 2026

Authors

Abhijeet Ghanwat
Department of Mathematics University of Georgia Athens, GA United States

Dishant M Pancholi
Institute for Mathematical Sciences Chennai India

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Volume 26, issue 4 (2026)