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EnglishLet's define the i-th 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(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.
| Autori interni: | |
| Autori: | Sandro Manfredini; Simona Settepanella |
| Titolo: | On the Configuration Spaces of Grassmannian Manifolds |
| Anno del prodotto: | 2014 |
| Abstract: | Let's define the i-th 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(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. |
| Digital Object Identifier (DOI): | 10.5802/afst.1410 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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