Justin R. Smith
Published 2014-02-13, updated 2015-03-07Version 14
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.
Comments: 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
Steenrod coalgebras III. The fundamental group
$\mathfrak{S}$-coalgebras determine fundamental groups
Steenrod coalgebras
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