Allowable singular simplex
= Allowable singular simplex
= Allowable singular simplices
{synonym}
An $i$-dimensional <singular simplex> $\sigma:\Delta^i\to X$ is $\bar p$-allowable if $\sigma^{-1}(X_{N-k})$ is contained in the $(i-k+\bar p(k))$-skeleton of $\Delta^i$ for every $k\ge2$. A negative skeleton is empty. Individual faces need not be allowable; this is why the definition of <intersection chains> separately imposes allowability on the total boundary.