Date & Time: Wednesday, March 09, 2016, 16:00-17:00.
Venue: Ramanujan Hall
Title: Morphisms of affine curves into homogeneous spaces
Abstract: Let X be an affine curve G, a connected reductive algebraic group and H a connected closed reductive algebraic subgroup. Assume that either the coordinate ring C[X] is a unique factorization domain or that H is semisimple. Let M (X, G/H) be the set of morphisms of X in G/H and C(X, G/H) the space of all continuous maps of X in G/H equipped the topology of uniform convergence on compact sets where X and G/H are given the Hausdorff topology. The set M (X, G/H) is in a natural fashion the inductive limit of affine varieties and can be given the inductive limit of the Hausdorff topologies on these varieties. Then the natural incusion of M (X, G/H) in C(X, G/H) is a homotopy equivalence.