Geodesic
Rational acyclic resolutions
Levin, Michael1
1Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel
Algebraic and Geometric Topology, Tome 5 (2005) no. 1, pp. 219-235
Cet article a éte moissonné depuis la source Mathematical Sciences Publishers

Voir la notice de l'article

Let X be a compactum such that dimℚX ≤ n, n ≥ 2. We prove that there is a ℚ–acyclic resolution r: Z→X from a compactum Z of dim ≤ n. This allows us to give a complete description of all the cases when for a compactum X and an abelian group G such that dimGX ≤ n, n ≥ 2 there is a G–acyclic resolution r: Z→X from a compactum Z of dim ≤ n.

DOI : 10.2140/agt.2005.5.219
Keywords: cohomological dimension, acyclic resolution

Levin, Michael  1

1 Department of Mathematics, Ben Gurion University of the Negev, P.O.B. 653, Be’er Sheva 84105, Israel 
@article{10_2140_agt_2005_5_219,
     author = {Levin, Michael},
     title = {Rational acyclic resolutions},
     journal = {Algebraic and Geometric Topology},
     pages = {219--235},
     year = {2005},
     volume = {5},
     number = {1},
     doi = {10.2140/agt.2005.5.219},
     url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.219/}
}
TY  - JOUR
AU  - Levin, Michael
TI  - Rational acyclic resolutions
JO  - Algebraic and Geometric Topology
PY  - 2005
SP  - 219
EP  - 235
VL  - 5
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.219/
DO  - 10.2140/agt.2005.5.219
ID  - 10_2140_agt_2005_5_219
ER  - 
%0 Journal Article
%A Levin, Michael
%T Rational acyclic resolutions
%J Algebraic and Geometric Topology
%D 2005
%P 219-235
%V 5
%N 1
%U http://geodesic.mathdoc.fr/articles/10.2140/agt.2005.5.219/
%R 10.2140/agt.2005.5.219
%F 10_2140_agt_2005_5_219
Levin, Michael. Rational acyclic resolutions. Algebraic and Geometric Topology, Tome 5 (2005) no. 1, pp. 219-235. doi: 10.2140/agt.2005.5.219

[1] R D Edwards, A theorem and a question related to cohomological dimension and cell-like maps (1978)

[2] A N Dranishnikov, On homological dimension modulo p, Mat. Sb. (N.S.) 132(174) (1987) 420, 446

[3] A N Dranishnikov, Extension of mappings into CW-complexes, Mat. Sb. 182 (1991) 1300

[4] A N Dranishnikov, Rational homology manifolds and rational resolutions, Topology Appl. 94 (1999) 75

[5] A Dranishnikov, Cohomological dimension theory of compact metric spaces, Topol. Atlas Inv. Contrib. 6 (2001) 7

[6] A Koyama, K Yokoi, Cohomological dimension and acyclic resolutions, Topology Appl. 120 (2002) 175

[7] M Levin, Acyclic resolutions for arbitrary groups, Israel J. Math. 135 (2003) 193

[8] M Levin, Universal acyclic resolutions for finitely generated coefficient groups, Topology Appl. 135 (2004) 101

[9] M Levin, Universal acyclic resolutions for arbitrary coefficient groups, Fund. Math. 178 (2003) 159

[10] J J Walsh, Dimension, cohomological dimension, and cell-like mappings, from: "Shape theory and geometric topology (Dubrovnik, 1981)", Lecture Notes in Math. 870, Springer (1981) 105

Cité par Sources :