On the category of Euclidean configuration spaces and associated fibrations
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.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2009
- DOI:
- 10.48550/arXiv.0904.1013
- arXiv:
- arXiv:0904.1013
- Bibcode:
- 2009arXiv0904.1013R
- Keywords:
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- Mathematics - Algebraic Topology;
- Mathematics - General Topology;
- 55M30;
- 55R80;
- 55S40
- E-Print:
- This is the version published by Geometry &