Trisecting non-Lagrangian theories

We propose a way to define and compute invariants of general smooth 4-manifolds based on topological twists of non-Lagrangian 4d N=20.5em and0.5em N=3 N = 2 and N = 3 theories in which the problem is reduced to a fairly standard computation in topological A-model, albeit with rather unusual targets, such as compact and non-compact Gepner models, asymmetric orbifolds, N=(2,2) N = 2 2 linear dilaton theories, “self-mirror” geometries, varieties with complex multiplication, etc.