Waldhausen’s classification theorem for finitely uniformizable 3-orbifolds

Takeuchi, Yoshihiro

doi:10.1090/S0002-9947-1991-1065604-3

Waldhausen’s classification theorem for finitely uniformizable $3$-orbifolds
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Trans. Amer. Math. Soc. 328 (1991), 151-200 Request permission

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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