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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
mathfrak{S}$-coalgebras determine fundamental groups
26 Jul 2013
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 $\pi_{1}(X)=\pi_{1}(Y)$.
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Details
- Title
- mathfrak{S}$-coalgebras determine fundamental groups
- Creators
- Justin R Smith
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- [Retired Faculty]
- Other Identifier
- 991021879757604721