Volume 16, issue 5 (2016)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Characteristic classes of fiber bundles

Takahiro Matsuyuki and Yuji Terashima

Algebraic & Geometric Topology 16 (2016) 3029–3050
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