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2011 Algebraic independence of generalized MMM–classes
Johannes Ebert
Algebr. Geom. Topol. 11(1): 69-105 (2011). DOI: 10.2140/agt.2011.11.69

Abstract

The generalized Miller–Morita–Mumford classes (MMM classes) of a smooth oriented manifold bundle are defined as the image of the characteristic classes of the vertical tangent bundle under the Gysin homomorphism. We show that if the dimension of the manifold is even, then all MMM–classes in rational cohomology are nonzero for some bundle. In odd dimensions, this is also true with one exception: the MMM–class associated with the Hirzebruch –class is always zero. Moreover, we show that polynomials in the MMM–classes are also nonzero. We also show a similar result for holomorphic fibre bundles and for unoriented bundles.

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Johannes Ebert. "Algebraic independence of generalized MMM–classes." Algebr. Geom. Topol. 11 (1) 69 - 105, 2011. https://doi.org/10.2140/agt.2011.11.69

Information

Received: 22 March 2010; Revised: 30 June 2010; Accepted: 23 September 2010; Published: 2011
First available in Project Euclid: 19 December 2017

zbMATH: 1210.55012
MathSciNet: MR2764037
Digital Object Identifier: 10.2140/agt.2011.11.69

Subjects:
Primary: 55R40

Rights: Copyright © 2011 Mathematical Sciences Publishers

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