EMBEDDINGS OF 4-MANIFOLDS IN S2 x S4 AND S2x S4 USING BORDERED LEFSCHETZ FIBRATION

In this paper, we discuss co-dimension 2 bordered achiral Lefschetz fibration (BALF) embeddings of bordered achiral Lefschetz fibrations over D-2 of a compact, connected, orientable 4{manifold with connected boundary into the trivial BALF of DE (m) x D-2 over D-2, where DE(m) is the 2-disc bundle over S-2 with the Euler number m: Using this, we show that the double of a BALF admits a smooth embedding in S-2 x S-4 as well as in S-2 x S-4. We also provide a huge collection of bordered achiral Lefschetz fibrations which admit BALF embeddings into the trivial Lefschetz fibration of D-4 x D-2 over D-2: Finally, we discuss BALF embeddings of non-orientable 4-manifolds X, where X does not admit 3{and 4{handles in the handle decomposition, into the trivial Lefschetz fibration of DE(m) x D-2 over D-2