Every closed orientable 3-manifold admits a codimension-1 spun embedding into a finite connected sum of S^2×S^2 and S^2~×S^2, constructed from sphere twists.
Handle decompositions and stabilizations of open books
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abstract
We build handle decompositions of n-manifolds that encode given open book decompositions and describe handle slides that reveal new open book decompositions on the same underlying manifold, for $n \geq 3$. This recovers known stabilization operations for open books. As an application, we show that any open book with trivial monodromy can be stabilized to an open book whose page is a boundary connected sum of trivial disk bundles over spheres.
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Twist maps and codimension-1 spun embeddings
Every closed orientable 3-manifold admits a codimension-1 spun embedding into a finite connected sum of S^2×S^2 and S^2~×S^2, constructed from sphere twists.