Abstract: It is proved that any π₁-finite-index map from a closed orientable 3-manifold covered by a torus bundle over S¹ to a closed aspherical orientable irreducible 3-manifold is homotopic to a covering map, and is of non-zero degree. This verifies a special case of the conjecture that any π₁-surjective map between closed aspherical 3-manifolds having the same rank on π₁ must be of non-zero degree.

Key words: π₁-finite-index map, torus bundle over S¹, aspherical 3-manifold, covering map, non-zero degree

摘要： 证明了任何从一个被圆周上的环面丛复迭的闭可定向三维流形到非球状的闭可定向不可约三维流形的基本群有限指数映射同伦于一个复迭映射，从而映射度非零。

关键词: 基本群有限指数映射, 圆周上的环面丛, 非球状三维流形, 复迭映射, 非零映射度