A classification of a class of 3-branchfolds

Takeuchi, Yoshihiro

doi:10.1090/S0002-9947-1988-0940214-4

A classification of a class of $3$-branchfolds
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by Yoshihiro Takeuchi PDF

Trans. Amer. Math. Soc. 307 (1988), 481-502 Request permission

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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