Nonzero degree maps between circle bundles over aspherical bases with strongly center-free fundamental groups are homotopic to fiber-preserving maps, yielding finiteness and a complete realization of finite mapping degree sets in all dimensions n>2.
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Maps between circle bundles: Fiber-preserving, Finiteness and Realization of mapping degree sets
Nonzero degree maps between circle bundles over aspherical bases with strongly center-free fundamental groups are homotopic to fiber-preserving maps, yielding finiteness and a complete realization of finite mapping degree sets in all dimensions n>2.