On the category of Euclidean configuration spaces and associated fibrations

2008/03/19 by Fridolin Roth · 1 citation
Decision Sciences · Mathematics · #Fuzzy and Soft Set Theory #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GN #msc:55M30 #msc:55R80 #msc:55S40

paper · pdf · doi:10.2140/gtm.2008.13.447

published as Geom. Topol. Monogr. 13 (2008) 447-461 · This is the version published by Geometry & Topology Monographs on 19 March 2008

openalex publication_date 2008/03/19 · arxiv created 2009/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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 piⁿ_k: F(Rⁿ,k) --> B(Rⁿ,k). We show that secat(piⁿ_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(piⁿ_k) precisely.

Citations

• On configuration spaces, their homology, and Lie algebras

Cited by

• Symmetric products, duality and homological dimension of configuration spaces

Related

• Configurations spaces and Theta_n
• The configuration category of a covering space
• Higher-categorical combinatorics of configuration spaces of Euclidean space
• Configuration spaces in algebraic topology
• Configuration spaces and Rⁿ