Earthman, Come Home: Cities in Flight Book 3

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.