Embeddings of 4-manifolds in S^4 × S^2 - Pandit, Suhas; A, Selvakumar (Topology Proceedings, 2023)
In this paper, we discuss simplified broken achiral Lefschetz fibration embeddings (SBLFE) of simplified broken achiral Lefschetz fibrations (SBLF) of compact, connected, oriented, smooth 4 -manifolds over D^2 into the trivial Lefschetz fibration of D E(1) × D^2 over D^2. Using this, we show that the double of an SBLF admits a smooth embedding in S^4 × S^2. Also, we provide broken achiral Lefschetz fibration (BLF) embeddings of a huge collection of BLF’s over S^2 into the trivial Lefschetz fibration of S^4 × S^2 over S^2. Finally, given a closed oriented smooth 4 -manifold Y, we provide BLF embeddings of a huge collection of BLF’s over S^2 into the trivial Lefschetz fibration of Y × S^2 over S^2.