An improvement in the linear stable ranges for ordered configuration spaces
Abstract
Recently, Church-Miller-Nagpal-Reinhold [arXiv:1706.03845] obtained linear stable ranges for the integral cohomology of ordered configuration spaces, in the sense of representation stability. We note that the constants in these linear stable ranges can be further improved for an orientable manifold of dimension at least 3. The idea is to simply exploit the sparsity of Totaro's spectral sequence.
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