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.

On the Configuration Spaces of Grassmannian Manifolds

Settepanella S
2014-01-01

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.
2014
Arrangements in Pyrenees
Pyrenees, France
11-15 Giugno 2012
Proceedings of the Conference Arrangements in Pyrenees
Toulouse University
23
2
353
359
https://afst.centre-mersenne.org/item/?id=AFST_2014_6_23_2_353_0
https://arxiv.org/abs/1311.5642
complex space, configuration spaces, braid groups
Manfredini S; Settepanella S
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2318/1843788
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