Characteristic classes of fiber bundles

Matsuyuki, Takahiro¹ ; Terashima, Yuji²

¹Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
²Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8552, Japan

Algebraic and Geometric Topology, Tome 16 (2016) no. 5, pp. 3029-3050

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.3029

Classification : 57R20, 55R40
Keywords: characteristic classes, fiber bundles, Chen expansions

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