Embeddings of 4-manifolds in $S^4 \tilde{\times} S^2$
Keywords:
4–manifolds, embeddings, Lefschetz fibrationAbstract
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 $\mathcal{D} E(1) \times D^2$ over $D^2$. Using this, we show that the double of an SBLF admits a smooth embedding in $S^4 \overline{\times} S^2$. 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 $S^4 \times S^2$ 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 $Y \times S^2$ over $S^2$.
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