Transferring curved $A_{\infty}$-structures and Chern classes

Details Transferring curved $A_{\infty}$-structures and Chern classes Transferring curved $A_{\infty}$-structures and Chern classes

2011-01-11

arxiv.org/abs/1101.2080v2

Mathematics

Differential Geometry

Scientific paper

We discuss how curved $A_{\infty}$- and $L_{\infty}$-algebras arise as deformations of $A_{\infty}$- and $L_{\infty}$-algebras and how the former structures can be transferred along chain contractions using homological perturbation theory. As an application, given vector bundle on a polyhedron $X$, we exhibit a curved $A_{\infty}$-structure on the complex of matrix-valued cochains of sufficiently fine triangulations of $X$. We use this structure as a motivation to develop a non-assosiative version of Chern-Weil theory.

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