Configuration spaces of an embedding torus and cubical spaces
Algebraic Topology
2007-05-23 v1 Geometric Topology
Abstract
For a smooth manifold M obtained as an embedding torus, A U Cx[-1,1], we consider the ordered configuration space F_k(M) of k distinct points in M. We show that there is a homotopical cubical resolution of F_k(M) defined from the configuration spaces of A and C. From it, we deduce a universal method for the computation of the pure braid groups of a manifold. We illustrate the method in the case of the Mobius band.
Keywords
Cite
@article{arxiv.math/0603496,
title = {Configuration spaces of an embedding torus and cubical spaces},
author = {Jean-Philippe Jourdan},
journal= {arXiv preprint arXiv:math/0603496},
year = {2007}
}
Comments
25 pages