Steenrod coalgebras of simplicial complexes

Abstract

In this paper, we extend earlier work by showing that if $X$ and $Y$ are simplicial complexes (i.e. simplicial sets whose simplices are determined by their vertices), a morphism $g:N(X)\to N(Y)$ of Steenrod coalgebras (normalized chain-complexes equipped with extra structure) induces one of their topological realizations $\hat{g}:|X|\to |Y|$. If $g$ is an isomorphism, then it induces an isomorphism between $X$ and $Y$, implying that they are homeomorphic.

17 pages. Since arXiv:1401.3618 is being published in Topology and its Applications, I have replaced all overlapping material with references to that paper. arXiv admin note: text overlap with arXiv:1403.1973