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TAUTOLOGICAL RINGS AND STABILISATION

Part of: Fiber spaces and bundles Differential topology

Published online by Cambridge University Press:  17 March 2021

OSCAR RANDAL-WILLIAMS
OSCAR RANDAL-WILLIAMS*
Affiliation:
Centre for Mathematical Sciences, Wilberforce Road, CambridgeCB3 0WB, UK e-mails: [email protected]
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Abstract

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We construct a ring homomorphism comparing the tautological ring, fixing a point, of a closed smooth manifold with that of its stabilisation by S2a×S2b.

MSC classification

Primary: 55R40: Homology of classifying spaces, characteristic classes
Secondary: 57R22: Topology of vector bundles and fiber bundles
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 64 , Issue 1 , January 2022 , pp. 231 - 242
Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2021. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

References

Allday, C. and Puppe, V., Cohomological methods in transformation groups, Cambridge Studies in Advanced Mathematics, vol. 32 (Cambridge University Press, 1993).Google Scholar
Baraglia, D., Tautological classes of definite 4-manifolds, arXiv:2008.04519, 2020.Google Scholar
Becker, J. C. and Gottlieb, D. H., The transfer map and fiber bundles, Topology 14(1) (1975), 1–12.CrossRefGoogle Scholar
Bustamante, M., Farrell, F. T. and Jiang, Y., Rigidity and characteristic classes of smooth bundles with nonpositively curved fibers, J. Topol. 9(3) (2016), 934–956.CrossRefGoogle Scholar
Faber, C., A conjectural description of the tautological ring of the moduli space of curves, Moduli of Curves and Abelian Varieties, Aspects Mathematics, E33 (Vieweg, Braunschweig, 1999), 109–129.Google Scholar
Galatius, S., Grigoriev, I. and Randal-Williams, O., Tautological rings for high-dimensional manifolds, Compos. Math. 153(4) (2017), 851–866.CrossRefGoogle Scholar
Giansiracusa, J., Kupers, A. and Tshishiku, B., Characteristic classes of bundles of K3 manifolds and the Nielsen realization problem, Tunis. J. Math. 3(1) (2021), 75–92.CrossRefGoogle Scholar
Grigoriev, I., Relations among characteristic classes of manifold bundles, Geom. Topol. 21(4) (2017), 2015–2048.Google Scholar
Hebestreit, F., Land, M., Lück, W. and Randal-Williams, O., A vanishing theorem for tautological classes of aspherical manifolds, Geom. Topol. 25(1) (2021), 47–110. doi: 10.2140/gt.2021.25.47 Google Scholar
Looijenga, E., On the tautological ring of Mg, Invent. Math. 121(2) (1995), 411–419.CrossRefGoogle Scholar
Morita, S., Generators for the tautological algebra of the moduli space of curves, Topology 42(4) (2003), 787–819.CrossRefGoogle Scholar
Mumford, D., Towards an enumerative geometry of the moduli space of curves, Arithmetic and Geometry, vol. II, Progress in Mathematics, vol. 36 (Birkhäuser, Boston, MA, 1983), 271–328.Google Scholar
Prigge, N., Tautological rings of fibrations, arXiv:1905.02676, 2019.Google Scholar
Randal-Williams, O., Some phenomena in tautological rings of manifolds, Selecta Math. (N.S.) 24(4) (2018), 3835–3873.CrossRefGoogle Scholar