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A topological space $X$ is $\mathbb Z$-formal, if the singular cochain complex $C^*(X,\mathbb Z)$ is quasi-isomorphic to $H^*(X, \mathbb Z)$ as an augmented differential graded ring. It's quite ...

Suppose we are given a map $f:A \rightarrow B$ between two dg-algebras which are formal. Is the map $f$ also "formal" in some sense? More precisely can we find isomorphisms $\phi_A:A\rightarrow H^\...

First let $L^{\bullet}$ be a pro-nilpotent differential graded Lie algebra (dgla). We have the set of Maurer-Cartan elements in $L^{\bullet}$ ($MC(L^{\bullet})$) which are $\alpha \in L^1$ such that ...