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INVARIANCE PROPERTIES OF MILLER-MORITA-MUMFORD CHARACTERISTIC NUMBERS OF FIBRE BUNDLES / T Church; M Crossley; J Giansiracusa

The Quarterly Journal of Mathematics

Swansea University Author: Giansiracusa, Jeffrey

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DOI (Published version): 10.1093/qmath/has029

Abstract

Characteristic classes of fibre bundles E^(d+n)→B^n in the category of closed oriented manifolds give rise to characteristic numbers by integrating the classes over the base. Church–Farb–Thibault raised the question of which generalized Miller–Morita–Mumford (MMM) classes have the property that the...

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Published in: The Quarterly Journal of Mathematics
ISSN: 0033-5606 1464-3847
Published: 2012
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URI: https://cronfa.swan.ac.uk/Record/cronfa13606
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Abstract: Characteristic classes of fibre bundles E^(d+n)→B^n in the category of closed oriented manifolds give rise to characteristic numbers by integrating the classes over the base. Church–Farb–Thibault raised the question of which generalized Miller–Morita–Mumford (MMM) classes have the property that the associated characteristic number is independent of the fibring and depends only on the bordism class of the total space E. Here, we determine a complete answer to this question in both the oriented category and the stably almost complex category. An MMM class has this property if and only if it is a fibre integral of a vector bundle characteristic class that satisfies a certain approximate version of the additivity of the Chern character.
College: College of Science