Orbi-maps and 3-orbifolds (Q917087)

The author announces three theorems on 3-orbifolds which mimic well-known results of 3-manifold topology. Let M and N be compact, ``good'' 3- orbifolds (i.e. orbit spaces of 3-manifolds with respect to properly discontinuous group actions). The first theorem is on representing a homomorphism \(\pi_ 1M\to \pi_ 1N\) by an orbi-map (a concept defined in this paper) \(M\to N\), the second one is on approximating an orbi-map \(M\to N\) by one which is transverse to a 2-suborbifold of N, and the third one is on representing an isomorphism \(\pi_ 1M\to \pi_ 1N\) by an orbi-isomorphism \(M\to N\). Two applications to links and tangles are included.