There's lots of confusion above.
The OP is correct in saying that the cracked glass he has is not the digitiser (which respondes to finger-tips) because that still works. The LED screen (see https://en.wikipedia.org/wiki/AMOLED for example) which creates the image is under the digitiser. Other layers like backlight, adhesive etc can exist and the LED itself is made of at least three layers - depending on what you count as a layer. Whether the layers can be separated or not depends on how its been put together and with what glue.
I'm just picking away at a broken front glass (only) on a Galaxy S7 edge, using acetone to soften the glue fixing it to the digitiser.