Abstract: In a recent paper, A. Reid, Shicheng Wang and Qing Zhou proved the following theorem: Let M₁ and M₂ be two closed aspherical Seifert 3-manifolds, whose fundamental groups have same rank. If the map f: M₁→M₂ is (π₁-surjective, i.e. f*π₁(M₁)=π₁(M₂), then f is of non-zero degree. Using this result, they also constructed a minimal Haken manifold and studied the epimorphism between the fundamental groups of 3-manifolds. In this paper, we prove that if we replace the condition "π₁-surjective" by "π₁-finite index", i.e. [π₁(M₂) : f*π₁(M₁)]<∞, the conclusion degf≠0 remans true.

Key words: Seifert manifold, π₁-finite index, degree, squeeze

摘要： A.Reid, 王诗成和周青证明了如下定理：设M₁, M₂为两个闭的非球状三维Seifert流形且它们的基本群的秩相同，如果映射 f: M₁→M₂ 是π₁满射，那么它的映射度degf≠0。他们利用该定理构造出了一个极小的Haken流形，并研究了三维流形群之间的满同态。本文证明了：若把以上的条件“π₁满射”换成“π₁有限指数”，则结论degf≠0仍然成立。

关键词: Seifert流形, π₁有限指数, 映射度, 挤压