Vol. 301, No. 2, 2019

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Double graph complex and characteristic classes of fibrations

Takahiro Matsuyuki

Vol. 301 (2019), No. 2, 547–574
DOI: 10.2140/pjm.2019.301.547
Abstract

In this paper, we construct a double chain complex generated by certain graphs and a chain map from that to the Chevalley–Eilenberg double complex of the differential graded Lie algebra (dgl) of symplectic derivations on a free dgl. It is known that the target of the map is related to characteristic classes of fibrations. We can describe some characteristic classes of fibrations whose fiber is a 1-punctured even-dimensional manifold by linear combinations of graphs though the cohomology of the dgl of derivations.

Keywords
graph complex, characteristic class, derivation, fiber bundle
Mathematical Subject Classification 2010
Primary: 55R40
Secondary: 55P62
Milestones
Received: 17 June 2018
Revised: 1 January 2019
Accepted: 2 January 2019
Published: 24 October 2019
Authors
Takahiro Matsuyuki
Graduate School of Mathematical Sciences
University of Tokyo
Meguro
Tokyo
Japan