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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-3-1,
author = {Claudemir Aniz},
title = {Strong surjectivity of mappings of some 3-complexes into 3-manifolds},
journal = {Fundamenta Mathematicae},
volume = {189},
year = {2006},
pages = {195-214},
zbl = {1111.55001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-3-1}
}
Claudemir Aniz. Strong surjectivity of mappings of some 3-complexes into 3-manifolds. Fundamenta Mathematicae, Tome 189 (2006) pp. 195-214. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm192-3-1/