Tautological rings for high-dimensional manifolds
Cambridge University Press
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Galatius, S., Grigoriev, I., & Randal-Williams, O. (2017). Tautological rings for high-dimensional manifolds. Compositio Mathematica, 153 (4), 851-866. https://doi.org/10.1112/S0010437X16008332
We study tautological rings for high-dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^*$($M$) of those characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised Miller–Morita–Mumford classes. We completely describe these rings modulo nilpotent elements, when $M$ is a connected sum of copies of $S^n$ × $S^n$ for $n$ odd.
tautological ring, characteristic class
S.G. was partially supported by NSF grants DMS-1105058 and DMS-1405001, the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 682922), as well as the Danish National Research Foundation through the Centre for Symmetry and Deformation (DNRF92) and ERC-682992. O.R.W. was partially supported by EPSRC grant EP/M027783/1.
External DOI: https://doi.org/10.1112/S0010437X16008332
This record's URL: https://www.repository.cam.ac.uk/handle/1810/262219