Brokeback Mountain is actually a fictional place in the short story "Brokeback Mountain" by Annie Proulx. It is inspired by the Bighorn Mountains which is a sister range of the Rocky Mountains existing halfway between Mt. Rushmore and Yellowstone National Park. It is the location where Jack Twist and Ennis del Mar meet for the first time while working for Farm and Ranch Employment over the summer, making it extremely significant. 

"Dawn came glassy orange, stained from below by a gelatinous band of pale green. The sooty bulk of the mountain paled slowly until it was the same color as the smoke from Ennis's breakfast fire. The cold air sweetened, banded pebbles and crumbs of soil cast sudden pencil-long shadows, and the rearing lodgepole pines below them massed in slabs of somber malachite. During the dy Ennis looked across a great gulf and sometimes saw Jack, a small dot moving across a high meadow as an insect moves across a tablecloth. Jack, in his dark camp, saw Ennis as night fire, a red spark on the huge black mass of mountain."

"The mountain boiled with demonic energy, glazed with flickering broken-cloud light. ... As they descended the sope Ennis felt he was in a slow-motion, but headlong, irreversible fall."