Volume 13 (2008)

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On the category of Euclidean configuration spaces and associated fibrations

Fridolin Roth

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 kth 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 πnk:F(Rn,k)→ B(Rn,k). We show that secat(πnk) 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(πnk) 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
Fridolin Roth
Fachbereich Mathematik der Universität Hamburg
SPAZ
Bundesstrasse 55
20146 Hamburg
Germany
http://www.math.uni-hamburg.de/home/roth/