\(A_\infty \) Algebras and Modules: Unfiltered Case

In this chapter, we study the algebraic version of \(A_\infty \) spaces by taking the chain complex of an \(A_{\infty }\) -space which naturally gives rise to the structure of an \(A_{\infty }\) algebra. We provide a quick review on well-known basic materials on the right \(A_\infty \) modules and their homomorphisms in Sects. 2.1–2.6 for the unfiltered case with nonzero curvature, i.e., allowing \(\mathfrak m_0\) to be non-vanishing.