Characteristic classes of fiber bundles

Matsuyuki, Takahiro; Terashima, Yuji

doi:10.2140/agt.2016.16.3029

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Characteristic classes of fiber bundles

Takahiro Matsuyuki and Yuji Terashima

Algebraic & Geometric Topology 16 (2016) 3029–3050

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.

Keywords

characteristic classes, fiber bundles, Chen expansions

Mathematical Subject Classification 2010

Primary: 57R20

Secondary: 55R40

References

Publication

Received: 4 December 2015

Revised: 14 March 2016

Accepted: 28 March 2016

Published: 7 November 2016

Authors

Takahiro Matsuyuki
Department of Mathematics Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan

Yuji Terashima
Department of Mathematical and Computing Sciences Tokyo Institute of Technology 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan

Volume 16, issue 5 (2016)