Geometry & Topology Monographs 13 (2008) 447–461

DOI: 10.2140/gtm.2008.13.447

arXiv: 0904.1013

Abstract

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

Keywords

Schwarz genus, sectional category, Lusternik–Schnirelmann category, category weight, configuration spaces

Mathematical Subject Classification

Primary: 55M30

Secondary: 55R80, 55S40

References

Publication

Received: 31 May 2006
Revised: 22 March 2007
Accepted: 29 March 2007
Published: 19 March 2008

Authors