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Stable moduli spaces of high-dimensional manifolds

Søren Galatius Department of Mathematics, Stanford University Oscar Randal-Williams Department of Pure Mathematics and Mathematical Statistics, University of Cambridge

Geometric Analysis and Geometric Topology mathscidoc: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.
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@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.
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