Title: On diagrams of simplified trisections and mapping class groups,
Abstract: A simplified trisection is a trisection map on a 4-manifold such that, in its
critical value set, there is no double point and cusps only appear in triples
on innermost fold circles. We give a necessary and sufficient condition for a
3-tuple of systems of simple closed curves in a surface to be a diagram of a
simplified trisection in terms of mapping class groups. As an application of
this criterion, we show that trisections of spun 4-manifolds due to Meier are
diffeomorphic (as trisections) to simplified ones. Baykur and Saeki recently
gave an algorithmic construction of a simplified trisection from a directed
broken Lefschetz fibration. We also give an algorithm to obtain a diagram of a
simplified trisection derived from their construction.