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

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