Lefschetz Open Book Embeddings of 4-Manifolds

In this article, we define the notion of a generalized open book of a n-manifold over the k−sphere Sk , k < n. We discuss Lefschetz open book embeddings of Lefschetz open books of closed oriented 4-manifolds into the trivial open book over S2 of the 7−sphere S7 . If X is the double of a bounded achiral Lefschetz fibration over D2 , then X naturally admits a Lefschetz open book given by the bounded achiral Lefschetz fibration. We show that this natural Lefschetz open book of X admits a Lefschetz open book embedding into the trivial open book over S2 of the 7−sphere S7 .