Homotopy theory of $C_{\infty }$-algebras and characteristic classes of fiber bundles

Abstract

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.

16 pages. New examples have been added. The title has been changed. Typos have been fixed