An $A_{\infty }$-coalgebra Structure on a Closed Compact Surface

Quinn Minnich, Ronald Umble

Let $P$ be an $n$-gon with $n\ge 3.$ There is a formal combinatorial $A_{\infty }$-coalgebra structure on cellular chains $C_{\ast }(P)$ with non-vanishing higher order structure when $n\ge…