Ditto on the Loctite 420 (another similar glue is Hot Stuff CA glue-- available at Woodcraft stores. Comes in 3 different viscosities, I think. You'll want the thinnest [watery-est] one so that it can wick deep into the damaged area). Both Loctite 420 and Hot Stuff are CA (cyanoacrylate) glues-- high-quality super glue.
Put some in/on the damaged area, let it work its way into the crack, maybe put on a little more if it all wicks in, wipe of any excess, and clamp to squeeze the damaged area back together to its original thickness. Be careful not to over-clamp-- don't want to do further damage. Let the glue set up for several hours or overnight. remove clamp, and use very fine (300-400 grit) sandpaper to smooth the repaired area. A little Minwax wipe-on polyurethane on the repaired area to match the surrounding finish, and you're good to go.