# MathSciDoc: An Archive for Mathematician ∫

#### Geometric Analysis and Geometric Topologymathscidoc:1701.15001

Acta Mathematica, 212, (2), 257-377, 2012.9
We prove an analogue of the Madsen–Weiss theorem for high-dimensional manifolds. In particular, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of$g$copies of$S$^{$n$}×$S$^{$n$}, in the limit $${g \to \infty}$$ . Rationally it is a polynomial ring in certain explicit generators, giving a high-dimensional analogue of Mumford’s conjecture.
@inproceedings{søren2012stable,
title={Stable moduli spaces of high-dimensional manifolds},
author={Søren Galatius, and Oscar Randal-Williams},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402807083788},
booktitle={Acta Mathematica},
volume={212},
number={2},
pages={257-377},
year={2012},
}

Søren Galatius, and Oscar Randal-Williams. Stable moduli spaces of high-dimensional manifolds. 2012. Vol. 212. In Acta Mathematica. pp.257-377. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203402807083788.