Some analogs of Zariski's Theorem on nodal line arrangements.
Strong surjectivity of mappings of some 3-complexes into 3-manifolds
Let K be a CW-complex of dimension 3 such that H³(K;ℤ) = 0, and M a closed manifold of dimension 3 with a base point a ∈ M. We study the problem of existence of a map f: K → M which is strongly surjective, i.e. such that MR[f,a] ≠ 0. In particular if M = S¹ × S² we show that there is no f: K → S¹ × S² which is strongly surjective. On the other hand, for M the non-orientable S¹-bundle over S² there exists a complex K and f: K → M such that MR[f,a] ≠ 0.
Strong surjectivity of mappings of some 3-complexes into
Let K be a CW-complex of dimension 3 such that H 3(K;ℤ) = 0 and the orbit space of the 3-sphere with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ . Given a point a ∈ , we show that there is no map f:K → which is strongly surjective, i.e., such that MR[f,a]=min(g −1(a))|g ∈ [f] ≠ 0.
Structural Theorems for Topological Actions of Z...-Tori on Real, Complex and Quarternionic Projective Spaces