  We give an explicit construction of the Honda--Kazez--Mati\'c gluing maps in
terms of contact handles. We use this to prove a duality result for turning a
sutured manifold cobordism around, and to compute the trace in the sutured
Floer TQFT. We also show that the decorated link cobordism maps on the hat
version of link Floer homology defined by the first author via sutured manifold
cobordisms and by the second author via elementary cobordisms agree.
