Abstract
Let K be a CW-complex of dimension 3 such that H 3(K;ℤ) = 0 and \( M_{Q_8 } \) the orbit space of the 3-sphere \( \mathbb{S}^3 \) with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ \( \mathbb{S}^3 \). Given a point a ∈ \( M_{Q_8 } \), we show that there is no map f:K → \( M_{Q_8 } \) which is strongly surjective, i.e., such that MR[f,a]=min{#(g −1(a))|g ∈ [f]} ≠ 0.
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Aniz, C. Strong surjectivity of mappings of some 3-complexes into \( M_{Q_8 } \) . centr.eur.j.math. 6, 497–503 (2008). https://doi.org/10.2478/s11533-008-0042-8
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DOI: https://doi.org/10.2478/s11533-008-0042-8