Gaitsgory, Dennis. 2012. “Contractibility of the Space of Rational Maps.” Invent. Math. 191 (1) (March 7): 91–196. doi:10.1007/s00222-012-0392-5.
We define an algebro-geometric model for the space of rational maps from a smooth curve X to an algebraic group G, and show that this space is homologically contractible. As a consequence, we deduce that the moduli space BunG of G-bundles on X is uniformized by the appropriate rational version of the affine Grassmannian, where the uniformizing map has contractible fibers.