Branched coverings of 2-complexes and diagrammatic reducibility

Gersten, S. M.

doi:10.1090/S0002-9947-1987-0902792-X

Branched coverings of $2$-complexes and diagrammatic reducibility
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by S. M. Gersten

Trans. Amer. Math. Soc. 303 (1987), 689-706

DOI: https://doi.org/10.1090/S0002-9947-1987-0902792-X

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Abstract:

The condition that all spherical diagrams in a $2$-complex be reducible is shown to be equivalent to the condition that all finite branched covers be aspherical. This result is related to the study of equations over groups. Furthermore large classes of $2$-complexes are shown to be diagrammatically reducible in the above sense; in particular, every $2$-complex has a subdivision which admits a finite branched cover which is diagrammatically reducible.

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