Handle decompositions and stabilizations of open books

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 $n\ge 3$. 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.

arXiv comment19 pages, 10 figures