DENVER — America’s suburbs are today’s great political battleground, long seen as an independent pivot between the country’s liberal cities and conservative small towns and rural expanse. But it’s not that simple. It turns out that these places in-between may be the most politically polarized of all — and when figuring out the partisan leanings of people living in the suburbs, where they came from makes a difference. Fewer suburbanites describe themselves as politically independent than do residents of the nation’s urban and rural areas, according to a survey released Tuesday by the University of Chicago Harris School for Public Policy and The Associated Press-NORC Center for Public Affairs Research.