Identify book - conflict between humans on sublight ship

I read the book in the last 5 years. My recollection is that it was written by one of the 2-tier masters of the Science Fiction genre.

The book starts as the person title "Teacher" is decanted. The ship warns him to evacuate the region of the ship. Teacher keeps barely escaping ruined portions of the ship as each section is sealed. He sometimes watches as others also decanted die in vacuum.

The book reveals the ship is three cylinders in the shadow of a giant ball of deuterium fuel. The ship is headed towards another star. Two factions are fighting for control of the ship. They are fighting over what to do when they get to the destination star system if intelligent life already exists there.

At least one cylinder is completely trashed and the cylinder in which Teacher was decanted is in very bad shape. Teacher and the ragtag group he recruits along the way go to the third cylinder to find answers and eventually confront the leader of one of the factions.