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

TL;DR

This paper develops a homotopy-theoretic approach to constructing characteristic classes of fiber bundles using $C_inf$-algebras, extending classical methods with a novel algebraic perspective.

Contribution

It introduces a Chern-Weil-type construction for fiber bundle characteristic classes based on homotopy theory of $C_inf$-algebras, replacing manifolds with algebraic morphisms.

Findings

Provides a new algebraic framework for characteristic classes

Extends classical Chern-Weil theory to $C_inf$-algebras

Establishes a homotopy-theoretic method for fiber bundle invariants

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.