Trisecting a 4-dimensional book into three chapters - Kegel, Marc; Schmäschke, Felix (Geometriae dedicata, 2024)
We describe an algorithm that takes as input an open book decomposition of a closed oriented 4-manifold and outputs an explicit trisection diagram of that 4-manifold. Moreover, a slight variation of this algorithm also works for open books on manifolds with non-empty boundary and for 3-manifold bundles over $$S^1$$. We apply this algorithm to several simple open books, demonstrate that it is compatible with various topological constructions, and argue that it generalizes and unifies several previously known constructions.