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arXiv · 1307.7098

$\mathfrak{S}$-coalgebras determine fundamental groups

Justin R. Smith
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Abstract

In this paper, we extend earlier work by showing that if $X$ and $Y$ are simplicial complexes (i.e. simplicial sets whose nondegenerate simplices are determined by their vertices), an isomorphism $\mathcal{C}(X)\cong\mathcal{C}(Y)$ of coalgebras over the Barratt-Eccles operad implies that the 3-skeleton of $X$ is weakly equivalent to the 3-skeleton of $Y$, also implying that $π_{1}(X)=π_{1}(Y)$.

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Justin R. Smith. 2013-08-12. $\mathfrak{S}$-coalgebras determine fundamental groups. https://arxiv.org/abs/1307.7098

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