On the Configuration Spaces of Grassmannian Manifolds
Sandro Manfredini, Simona Settepanella (2014)
Annales de la faculté des sciences de Toulouse Mathématiques
Similarity:
Let be the -th ordered configuration space of all distinct points in the Grassmannian of -dimensional subspaces of , whose sum is a subspace of dimension . We prove that is (when non empty) a complex submanifold of of dimension and its fundamental group is trivial if , and and equal to the braid group of the sphere if . Eventually we compute the fundamental group in the special case of hyperplane arrangements, i.e. .