2012/19 | LEM Working Paper Series | |
On the Configuration Spaces of Grassmannian Manifolds |
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Sandro Manfredini, Simona Settepanella |
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Keywords | ||
complex space, configuration spaces, braid groups
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JEL Classifications | ||
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Abstract | ||
Let's define the i-th ordered configuration space as the space of all
distinct points H1,...,Hh 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(n-i)+hk(i-k) 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=n-1.
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