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arXiv · 0904.1013

On the category of Euclidean configuration spaces and associated fibrations

Fridolin Roth
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Abstract

We calculate the Lusternik-Schnirelmann category of the k-th ordered configuration spaces F(R^n,k) of R^n and give bounds for the category of the corresponding unordered configuration spaces B(R^n,k) and the sectional category of the fibrations pi^n_k: F(R^n,k) --> B(R^n,k). We show that secat(pi^n_k) can be expressed in terms of subspace category. In many cases, eg, if n is a power of 2, we determine cat(B(R^n,k)) and secat(pi^n_k) precisely.

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Fridolin Roth. 2009-04-06. On the category of Euclidean configuration spaces and associated fibrations. https://doi.org/10.2140/gtm.2008.13.447

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