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2016 Characteristic classes of fiber bundles
Takahiro Matsuyuki, Yuji Terashima
Algebr. Geom. Topol. 16(5): 3029-3050 (2016). DOI: 10.2140/agt.2016.16.3029

Abstract

In this paper, we construct new characteristic classes of fiber bundles via flat connections with values in infinite-dimensional Lie algebras of derivations. In fact, choosing a fiberwise metric, we construct a chain map to the de Rham complex on the base space, and show that the induced map on cohomology groups is independent of the choice of metric. Moreover, we show that, applied to a surface bundle, our construction gives Morita–Miller–Mumford classes.

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Takahiro Matsuyuki. Yuji Terashima. "Characteristic classes of fiber bundles." Algebr. Geom. Topol. 16 (5) 3029 - 3050, 2016. https://doi.org/10.2140/agt.2016.16.3029

Information

Received: 4 December 2015; Revised: 14 March 2016; Accepted: 28 March 2016; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06653768
MathSciNet: MR3572358
Digital Object Identifier: 10.2140/agt.2016.16.3029

Subjects:
Primary: 57R20
Secondary: 55R40

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.16 • No. 5 • 2016
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