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Preprint
Steenrod coalgebras III. The fundamental group
arXiv.org
08 Mar 2014
Abstract
In this note, we extend earlier work by showing that if $X$ and $Y$ are
delta-complexes (i.e. simplicial sets without degeneracy operators), a morphism
$g:N(X)\to N(Y)$ of Steenrod coalgebras (normalized chain-complexes equipped
with extra structure) induces one of 2-skeleta $\hat{g}:X_{2}\to Y_{2}$,
inducing a homomorphism $\pi_{1}(\hat{g}):\pi_{1}(X)\to\pi_{1}(Y)$ that is an
isomorphism if $g$ is an isomorphism. This implies a corresponding conclusion
for a morphism $g:C(X)\to C(Y)$ of Steenrod coalgebras on unnormalized
chain-complexes of simplicial sets.
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Details
- Title
- Steenrod coalgebras III. The fundamental group
- Creators
- Justin R Smith
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- [Retired Faculty]
- Other Identifier
- 991021880180404721