2012/19  LEM Working Paper Series  
On the Configuration Spaces of Grassmannian Manifolds 

Sandro Manfredini, Simona Settepanella 

Keywords  
complex space, configuration spaces, braid groups


JEL Classifications  


Abstract  
Let's define the ith ordered configuration space as the space of all
distinct points H_{1},...,H_{h} in the complex Grassmannian Gr(k,n) whose
sum is a subspace of dimension i. We prove that this space is (when
non empty) a complex submanifold of Gr(k,n)^{h} of dimension
i(ni)+hk(ik) and its fundamental group is trivial if i=min(n,hk), hk
is different from n and n>2 and equal to the braid group of the sphere
if n=2. Eventually we compute the fundamental group in the special
case of hyperplane arrangements, i.e. k=n1.
 
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