Sharper periodicity and stabilization maps for configuration spaces of closed manifolds

TL;DR

This paper advances the understanding of the homology of configuration spaces in closed manifolds by improving periodicity results, establishing integral stability for odd-dimensional cases, and introducing a new stabilization map with specific coefficients.

Contribution

It refines periodicity results, proves integral homological stability for odd-dimensional manifolds, and introduces a new stabilization map with $Z[1/2]$-coefficients.

Findings

Sharpened periodicity results for configuration spaces

Proved integral homological stability for odd-dimensional manifolds

Introduced a stabilization map on homology with $Z[1/2]$-coefficients

Abstract

In this note we study the homology of configuration spaces of closed manifolds. We sharpen the eventual periodicity results of Nagpal and Cantero-Palmer, prove integral homological stability for configuration spaces of odd-dimensional manifolds and introduce a stabilization map on the homology with $Z[1/2]$-coefficients of configuration spaces of odd-dimensional manifolds.