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