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Waldhausen's Classification Theorem for Finitely Uniformizable 3-Orbifolds

Yoshihiro Takeuchi
Transactions of the American Mathematical Society
Vol. 328, No. 1 (Nov., 1991), pp. 151-200
DOI: 10.2307/2001880
Stable URL: http://www.jstor.org/stable/2001880
Page Count: 50
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Waldhausen's Classification Theorem for Finitely Uniformizable 3-Orbifolds
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Abstract

We define a map between two orbifolds. With respect to this map, we generalize 3-manifold theory to 3-orbifolds. As the main goal, we generalize the Waldhausen's classification theorem of Haken 3-manifolds to finitely uniformizable 3-orbifolds. For applications of the developed theory, we introduce an invariant for links and tangles by using the orbifold fundamental group. With the invariant, we classify a class of links and show the untangling theorem.

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