Scanning for oriented configuration spaces
Abstract
In [Pal13] (arXiv:1106.4540) the second author proved that the sequence of "oriented" configuration spaces on an open connected manifold exhibits homological stability as the number of particles goes to infinity. To complement that result we identify the corresponding limiting space, up to homology equivalence, as a certain explicit double cover of a section space. Along the way we also prove that the scanning map of McDuff in [McD75] for unordered configuration spaces is acyclic in the limit.
Cite
@article{arxiv.1306.6896,
title = {Scanning for oriented configuration spaces},
author = {Jeremy Miller and Martin Palmer},
journal= {arXiv preprint arXiv:1306.6896},
year = {2018}
}
Comments
v2: 32 pages. Version 1 has been split into two parts. This is the second part (corresponding to section 3 in v1), substantially revised and incorporating the referee's corrections and suggestions; to appear in Homology, Homotopy and Applications. The first part (corresponding to section 2 of v1) has been separated into the preprint arXiv:1409.4389