Clamping is the real bugaboo here. Several of the glues mentioned will work well if the shoe is clamped with
pressure on the entire sole. The mention of tape by one poster reminded me of methods used for odd shaped
wood glue ups, such as using a scrapped thin rubber inner tube. A good tight wrap with an inner tube should
apply fairly uniform pressure to the edges and center of a rigid sole. Have to remember this approach next
time one of my shoes tosses an outer sole. With a non-rigid sole a sole length piece square wood in the center
of the sole might suffice for pressure there, would require some experimentation.