π₁-finite-index Maps from 3-manifolds Covered by Torus Bundles over S^１

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

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