Formality of $A_\infty$-Algebras

TL;DR

This thesis explores the concept of formality in $A_ Infty$-algebras, providing foundational theory, a proof of a key transfer principle, and applications to K"ahler manifolds.

Contribution

It offers a direct proof of Kadeishvili's Theorem and applies homological perturbation theory to the study of $A_ Infty$-algebras and their formality.

Findings

Established a direct proof of the homotopy transfer principle for $A_ Infty$-algebras.

Demonstrated the formality of compact K"ahler manifolds.

Enhanced understanding of homological perturbation techniques in algebraic topology.

Abstract

This master's thesis contains an introduction to $A_\infty$-algebras and homological perturbation theory. We then discuss the formality of compact K\"ahler manifolds and present a direct proof of a homotopy transfer principle of $A_\infty$-algebras, also known as Kadeishvili's Theorem.