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Simplifying <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mn>3</mml:mn></mml:math>-manifolds in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>โ</mml:mi></mml:mrow> <mml:mn>4</mml:mn> </mml:msup></mml:math>
We show that a smooth embedding of a closed 3-manifold in S 3 รโ can be isotoped so that every generic level divides S 3 รt into two handlebodies (i.e., is Heegaard) provided the original embedding has a unique local maximum with respect to the โ coordinate. This allows uniqueness โฆ