The typical effect of bark inversion is 1) larger/better quality fruits 2) more flowers. However, the effect is not permanent, it must be repeated once new layers of cambium develop. The guy credited with promoting this technique is Karl Sax. A 1957 article from popular mechanics describes his antics – (Popular Mechanics - Vol. 107, No. 2, p 113). This article has already been posted here –
I get a bit of a sick feeling in my stomach seeing him tie those apples into knots, much akin to the same feeling when I see a wolf pacing back and forth in a zoo cage.
This study by Arakawa et al – is a nice demonstration of increase in fruiting wood development and better fruit quality:
"Effects of Five Methods of Bark Inversion and Girdling on the Tree Growth and Fruit Quality of ‘Megumi’ Apple. "Journal of the Japanese Society for Horticultural Science. Vol. 67 (1998) No. 5 P 721-727
One interesting thing they do is bark exchange between cultivars. What I’d like to try is exchanging the bark from a dwarfing rootstock or natural dwarf apple. A slight incompatibility between the topstock and the exchange bark would, I theorize, cause the dwarfing effect to be permanent. Effectively this would be a interstem graft added ‘after the fact.’