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Curved $A_{\infty}$-algebras and Chern classes by Nikolov, Nikolay M.; Zahariev, Svetoslav is a scholarly article available to read on EtoBox.

What is Curved $A_{\infty}$-algebras and Chern classes about?

We describe two constructions giving rise to curved $A_{\infty}$-algebras. The first consists of deforming $A_{\infty}$-algebras, while the second involves transferring curved dg structures that are deformations of (ordinary) dg structures along chain contractions. As an application of the second construction, given a 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 homotopy associative version of Chern-Weil theory.

Author

Nikolov, Nikolay M.; Zahariev, Svetoslav

Published

2011

Language

EN