A Kuenneth theorem for configuration spaces
Algebraic Topology
2022-03-09 v2
Abstract
We construct a spectral sequence converging to the homology of the ordered configuration spaces of a product of parallelizable manifolds. To identify the second page of this spectral sequence, we introduce a version of the Boardman--Vogt tensor product for linear operadic modules, a purely algebraic operation. Using the rational formality of the little cubes operads, we show that our spectral sequence collapses in characteristic zero.
Cite
@article{arxiv.1810.02249,
title = {A Kuenneth theorem for configuration spaces},
author = {Kathryn Hess and Ben Knudsen},
journal= {arXiv preprint arXiv:1810.02249},
year = {2022}
}
Comments
21 pages. To appear in the Journal of the London Mathematical Society. May differ slightly from published version