Characteristic classes of fiber bundles

Takahiro Matsuyuki, Yuji Terashima

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)3029-3050
Number of pages22
JournalAlgebraic and Geometric Topology
Volume16
Issue number5
DOIs
Publication statusPublished - 2016 Nov 7

Keywords

  • Characteristic classes
  • Chen expansions
  • Fiber bundles

ASJC Scopus subject areas

  • Geometry and Topology

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