I hosed a up a delicate piece of oak I was working on with the jigsaw. The
cut is fine, but as I was making it the slim section I was working on just
fell off - like it'd been cut by an inviisible blade. Hacked me off, as it
was my own fault for not supporting it well enough. Very VERY clean break,
smoother than a baby's bottom but I'm wondering if I need to do anything
with both ends before glueing it together and praying it will hold.

Do I need to allow for expansion in the glue when I attempt to assemble the
pieces or will the glue not add any appreciable dimension to the joint?
Presumably I won't be slathering it on like peanut butter.