You can use fiber glass cloth and fiber glass resin
It will hold everything together nicely. It won't separate from the part later if you clean all of the surfaces enthusiastically. It's easy.
I recommend getting some disposable gloves to use while you do this.
Once you have the bits in pieces in place properly you can line the inside with some fiber glass cloth that has been completely immersed in fiber glass resin. Push it up into the inside portion of the cracked carbon fiber component. You can also wipe some of the resin into the outside crack.
I typically dry my parts in an oven I have in the garage. Don't do it in your house, the vapors that come off the resin as it dries are harmful. The heat accelerates the hardening.
Once the resin is dry and hard you can sand it down and buff it up a bit to make it look a little better. Since it's a track bike it might not matter or be worth the time since it might get broken again soon anyway.
I've done this many, many times on CF parts for play bikes. It's strong, easy, simple, fast (once you've done it a couple of times) and CHEAP.