Characteristic numbers of manifold bundles over surfaces with highly connected fibers

We study smooth bundles over surfaces with highly connected almost parallelizable fiber M of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases, these conditions are also sufficient. Using this, we determine...

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Veröffentlicht in:	Journal of the London Mathematical Society 2020-10, Vol.102 (2), p.879-904
Hauptverfasser:	Krannich, Manuel, Reinhold, Jens
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Sprache:	eng
Schlagworte:	55R10 55R40 (primary) 57R20 57R75 (secondary)
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creator	Krannich, Manuel Reinhold, Jens
description	We study smooth bundles over surfaces with highly connected almost parallelizable fiber M of even dimension, providing necessary conditions for a manifold to be bordant to the total space of such a bundle and showing that, in most cases, these conditions are also sufficient. Using this, we determine the characteristic numbers realized by total spaces of bundles of this type, deduce divisibility constraints on their signatures and Â‐genera, and compute the second integral cohomology of BDiff+(M) up to torsion in terms of generalized Miller–Morita–Mumford classes. We also prove analogous results for topological bundles over surfaces with fiber M and discuss the resulting obstructions to smoothing them.
doi_str_mv	10.1112/jlms.12344
format	Article
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title	Characteristic numbers of manifold bundles over surfaces with highly connected fibers
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