Algebraic & Geometric Topology

Characteristic classes of fiber bundles

Takahiro Matsuyuki and Yuji Terashima

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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.agt/1510841238

Digital Object Identifier
doi:10.2140/agt.2016.16.3029

Mathematical Reviews number (MathSciNet)
MR3572358

Zentralblatt MATH identifier
06653768

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

Keywords
characteristic classes fiber bundles Chen expansions

Citation

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. https://projecteuclid.org/euclid.agt/1510841238


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