Homotopy theory of $C_\infty$-algebras and characteristic classes of   fiber bundles
  In this paper we give a Chern-Weil-type construction of characteristic classes of fiber bundles, based on homotopy theory of C-infinity algebras. Our idea is to replace a family of closed manifolds to a family of C-infinity morphisms with family of metrics. 
Hiroshige Kajiura, Takahiro Matsuyuki, and Yuji Terashima
math.GT