Algebraic & Geometric Topology

Characteristic classes of fiber bundles

Takahiro Matsuyuki and Yuji Terashima

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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.

Article information

Algebr. Geom. Topol., Volume 16, Number 5 (2016), 3029-3050.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57R20: Characteristic classes and numbers
Secondary: 55R40: Homology of classifying spaces, characteristic classes [See also 57Txx, 57R20]

characteristic classes fiber bundles Chen expansions


Matsuyuki, Takahiro; Terashima, Yuji. Characteristic classes of fiber bundles. Algebr. Geom. Topol. 16 (2016), no. 5, 3029--3050. doi:10.2140/agt.2016.16.3029.

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