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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



A classification of a class of $ 3$-branchfolds

Author: Yoshihiro Takeuchi
Journal: Trans. Amer. Math. Soc. 307 (1988), 481-502
MSC: Primary 57N10; Secondary 57M12
MathSciNet review: 940214
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Abstract: An $ n$-orbifold is a topological space provided with a local modelling on (an open set in $ {{\mathbf{R}}^n}$)/(a finite group action). Mainly, we deal with $ 3$-branchfolds (i.e. $ 3$-orbifolds with $ 1$-dimensional singular locus). We define a map between two $ 3$-branchfolds. With respect to this map, we prove some facts parallel to $ 3$-manifold theorems. Using the facts, we classify a class of $ 3$-branchfolds, analogous to Waldhausen's classification theorem of Haken manifolds.

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Keywords: Branchfold, fundamental group of orbifolds, $ OR$-map
Article copyright: © Copyright 1988 American Mathematical Society