Barbu Berceanu, Muhammad Yameen: Strong and shifted stability for the cohomology of configuration spaces, 159-191

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 closed oriented manifolds with even cohomology, whose top Betti numbers are stable after a shift of degree.

Key Words: Unordered configuration spaces, homological stability, Knudsen model, Félix-Thomas model.

2010 Mathematics Subject Classification: Primary 55R80, 57N65, 57R19; Secondary 55P62.