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

 

Waldhausen's classification theorem for finitely uniformizable $ 3$-orbifolds


Author: Yoshihiro Takeuchi
Journal: Trans. Amer. Math. Soc. 328 (1991), 151-200
MSC: Primary 57M50; Secondary 57M12, 57M35
MathSciNet review: 1065604
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1065604-3
PII: S 0002-9947(1991)1065604-3
Keywords: Orbi-map, orbifold, finite uniformization
Article copyright: © Copyright 1991 American Mathematical Society