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arXiv · 1810.05011

Strong stability and shifted stability for the cohomology of configuration spaces

Barbu Berceanu·Muhammad Yameen
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Abstract

Homological stability for unordered configuration spaces of connected manifolds was discovered by Th. Church and extended by O. Randal-Williams and B. Knudsen: $H_i(C_k(M);\mathbb{Q})$ is constant for $k\geq f(i)$. We characterize the manifolds satisfying strong stability: $H^*(C_k(M);\mathbb{Q})$ is constant for $k\gg 0$. We give few examples of manifolds whose top Betti numbers are stable after a shift of degree.

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Barbu Berceanu, Muhammad Yameen. 2018-10-11. Strong stability and shifted stability for the cohomology of configuration spaces. https://arxiv.org/abs/1810.05011

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