A Kuenneth theorem for configuration spaces
arXiv:1810.02249 · doi:10.1112/jlms.12536
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.
21 pages. To appear in the Journal of the London Mathematical Society. May differ slightly from published version