The third volume of James Blish's SF classic CITIES IN FLIGHT
When the cities left Earth, they exchanged a simple environment for one of constant, sometimes shattering change. The Universe was littered with cultures in every conceivable stage of development. Only the iron hand of the germanium-backed economy and occasional interventions by the Earth police imposed some kind of order on the spaceways. Even John Amalfi never got used to the life - and he had been mayor of New York for nearly five hundred years now.
James Blish (1921-75) studied microbiology at Rutgers and then served as a medical laboratory technician in the US army during the Second World War. Among his best known books are Cities in Flight, A Case of Conscience, for which he won the Hugo in 1959 for Best Novel, Doctor Mirabilis, Black Easter and The Day After Judgement.