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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Branched coverings of $ 2$-complexes and diagrammatic reducibility


Author: S. M. Gersten
Journal: Trans. Amer. Math. Soc. 303 (1987), 689-706
MSC: Primary 57M12; Secondary 20F05, 57M20
MathSciNet review: 902792
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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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DOI: http://dx.doi.org/10.1090/S0002-9947-1987-0902792-X
PII: S 0002-9947(1987)0902792-X
Article copyright: © Copyright 1987 American Mathematical Society