There is a series of four science fiction books about a kid that learns how to teleport. The story begins with the main character (call him Jim for easier reference) and about 100 other children aged 13ish on a escape pod with a motherly AI that organized the children. Jim is able to telepathically connect to computers, and he can speak to the AI. He is bullied because the other kids think he makes it up.
Eventually the shuttle comes to a space station community for four arcs that orbit a black hole. The arcs were quarter circle curves that had their own gravity, sky and oxygen. Each arc has a different purpose. The first is mostly courts and database structures. The second is commercial/industrial, and the third or fourth is an elitist civilian arc, and I can't remember the other.
The children arrive at the courts and judging arc, and are deemed to travel the community, one arc per year. At the second arc, also the second book, the children are forced to work at a factory with dangerous equipment. Their guardian is a dual species, some creature that requires another to live inside it for it to live, a mutually beneficial relationship. Jim and a few friends have weird dreams in the sleepers and chase a girl in a forest. Somehow that's connected to the plot.
At the civilian arc the children are sent to school, where they dominate all other students because they are the only humans. Jim has to present to elitist civilians and gets stressed and jumps (teleports) to another location.
Jim is forced by a bully to break into a room, where the bully finds a belt, puts it on, and disappears.
Somehow he is sent to an asteroid and meets a man stuck in the wall that is his dad who jumped incorrectly. He learns that he needs the belt like the bully found, or one like it, to properly jump.
Jim and his friends are attacked by pirates. It turns out the pirate leader is the bully, now 40ish; he jumped into the future.
I can't remember anything else.