Strong surjectivity of mappings of some 3-complexes into 3-manifolds

Claudemir Aniz. "Strong surjectivity of mappings of some 3-complexes into 3-manifolds." Fundamenta Mathematicae 192.3 (2006): 195-214. <http://eudml.org/doc/283014>.

@article{ClaudemirAniz2006,
abstract = {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.},
author = {Claudemir Aniz},
journal = {Fundamenta Mathematicae},
keywords = {Surjective maps; Roots; Cohomology with local coefficients; Obstruction; Complexes with zero top cohomology},
language = {eng},
number = {3},
pages = {195-214},
title = {Strong surjectivity of mappings of some 3-complexes into 3-manifolds},
url = {http://eudml.org/doc/283014},
volume = {192},
year = {2006},
}

TY - JOUR
AU - Claudemir Aniz
TI - Strong surjectivity of mappings of some 3-complexes into 3-manifolds
JO - Fundamenta Mathematicae
PY - 2006
VL - 192
IS - 3
SP - 195
EP - 214
AB - 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.
LA - eng
KW - Surjective maps; Roots; Cohomology with local coefficients; Obstruction; Complexes with zero top cohomology
UR - http://eudml.org/doc/283014
ER -