On the category of Euclidean configuration spaces and associated fibrations

Details On the category of Euclidean configuration spaces and associated fibrations On the category of Euclidean configuration spaces and associated fibrations

2009-04-06

arxiv.org/abs/0904.1013v1

Geom. Topol. Monogr. 13 (2008) 447-461

Mathematics

Algebraic Topology

This is the version published by Geometry & Topology Monographs on 19 March 2008

Scientific paper

10.2140/gtm.2008.13.447

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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