Resumen:
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Let W4=H0??H1??H2??H3?H4 be a handle decomposition of a closed, orientable PL 4-manifold. Let M4=H0??H1??H2 and let N4=N4(?)=?H3?H4=?#(S1×B3). Then W4 is M4?N4, identified along ?M4=?N4=?#(S1×S2). The first observation in this paper is that W4 does not depend upon the method of attaching N4, as a consequence of a theorem of F. Laudenbach and V. Poénaru [Bull. Soc. Math. France 100 (1972), 337–344;], who showed (implicitly) that the homotopy group of ?N4 is generated by maps which extend to N4. Dually, W4 does not depend upon the method of attaching H0??H1?N4(?). Hence W4 depends only on the cobordism C(?,?) from ?#(S1×S2) to ?#(S1×S2) defined by the 2-handles. The author calls (W4,C(?,?)) a Heegaard splitting of W4. The associated Heegaard diagram is a pair (?#S1×S2,w) where w is a framed link in ?#S1×S2. It is noted that an arbitrary pair (?#S1×S2,w) need not be a Heegaard diagram for a 4-manifold.
Two diagrams are equivalent if there is a homeomorphism of pairs which preserves the framings. Moves are given which relate any two Heegaard diagrams for the same 4-manifold. The completeness of these moves is proved in Theorem 3 (and also Theorem 3?). A concept of a dual diagram is introduced. It is not known whether each Heegaard diagram is geometrically realizable as the diagram for some closed 4-manifold.
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