Contractibility of the space of rational maps

By D. Gaitsgory. 2011

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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 $\operatorname {Bun}_{G}$ of G-bundles on X is uniformized by the appropriate rational version of the affine Grassmannian, where the uniformizing map has contractible fibers.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b660e2024408919a0a4138f1bb72f7d65517d84a