New Worlds to Conquer. A Button in the Fabric of Time, #1

The universe contains billions upon billions of galaxies, and many of those galaxies contain multiple billions of planets. Perhaps, among those planets, there are worlds where people can reside. New Worlds to Conquer is a sequel to A Button in the Fabric of Time, about Gus, a twenty-first century engineer, who travels into the thirty-first century. There he meets a beautiful woman, marries her, and works with her to produce a-heaven on earth-where people never grow old.
To save Earth for productive use, people live in cities of glass, floating on the ocean. Each city contains forty levels, and people travel in transportation devices at the speed of thought. Robots do the work, but people supervise the robots. Gus and his wife Jan-3 are assigned the task of bringing people who have passed away in previous years into the future to populate other planets.