Strong surjectivity of mappings of some 3-complexes into M Q 8

Claudemir Aniz

Open Mathematics (2008)

  • Volume: 6, Issue: 4, page 497-503
  • ISSN: 2391-5455

Abstract

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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 𝕊 3 with respect to the action of the quaternion group Q 8 determined by the inclusion Q 8 ⊆ 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.

How to cite

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Claudemir Aniz. "Strong surjectivity of mappings of some 3-complexes into \[ M_{Q_8 } \]." Open Mathematics 6.4 (2008): 497-503. <http://eudml.org/doc/269337>.

@article{ClaudemirAniz2008,
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.},
author = {Claudemir Aniz},
journal = {Open Mathematics},
keywords = {strongly surjective map; cohomology with local coefficients; linear systems; quaternion group},
language = {eng},
number = {4},
pages = {497-503},
title = {Strong surjectivity of mappings of some 3-complexes into \[ M\_\{Q\_8 \} \]},
url = {http://eudml.org/doc/269337},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Claudemir Aniz
TI - Strong surjectivity of mappings of some 3-complexes into \[ M_{Q_8 } \]
JO - Open Mathematics
PY - 2008
VL - 6
IS - 4
SP - 497
EP - 503
AB - 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.
LA - eng
KW - strongly surjective map; cohomology with local coefficients; linear systems; quaternion group
UR - http://eudml.org/doc/269337
ER -

References

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