All Questions

Let $\varphi:A\to \mathrm{Ass}$ be an $A_\infty$-operad in topological spaces, and let $X$ be an $A$-algebra. I see three possibilities to construct a delooping out of $X$: Rectify $X$ by taking the ...

Let $A$ be an algebra over the brace tree operad and $M$ a module over some base ring. Is there a good notion of a "left brace module" over a brace algebra? I do not think the definition of a module ...

To describe homotopy invariant algebraic structures on spaces, there are different approaches. The Stasheff / Boardman–Vogt / May approach, where operations and equations are replaced by spaces of ...

Hello, I would like explanation or clear source for some things related to $A_{\infty}$-spaces, via Stasheff's polytopes. I tried not to think about them, because they seem too complicated for me; I ...

Informally, an $A_\infty$-space is a monoid whose laws are only satisfied up to homotopy. Let’s define now what I will call a "homotopic monoid" to be a space $M$ together with a point $e\in{}M$ and ...

Given a DGA $A$, then by standard techniques such as homological perturbation theory, the ring structure on the homology $H(A)$ extends to a minimal $A_\infty$-algebra structure such that $H(A)$ is ...