Geodesic
On dimension of product of groups
Algebra and discrete mathematics, Tome 28 (2019) no. 2, pp. 203-212.

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove the product formula $\operatorname{cd}(\Gamma\times\Gamma)=2\operatorname{cd}\Gamma$ for cohomological dimension of geometrically finite groups.
Keywords: product of groups, cohomological dimension. 
@article{ADM_2019_28_2_a5,
     author = {Alexander Dranishnikov},
     title = {On dimension of product of groups},
     journal = {Algebra and discrete mathematics},
     pages = {203--212},
     publisher = {mathdoc},
     volume = {28},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2019_28_2_a5/}
}
TY  - JOUR
AU  - Alexander Dranishnikov
TI  - On dimension of product of groups
JO  - Algebra and discrete mathematics
PY  - 2019
SP  - 203
EP  - 212
VL  - 28
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2019_28_2_a5/
LA  - en
ID  - ADM_2019_28_2_a5
ER  - 
%0 Journal Article
%A Alexander Dranishnikov
%T On dimension of product of groups
%J Algebra and discrete mathematics
%D 2019
%P 203-212
%V 28
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2019_28_2_a5/
%G en
%F ADM_2019_28_2_a5
Alexander Dranishnikov. On dimension of product of groups. Algebra and discrete mathematics, Tome 28 (2019) no. 2, pp. 203-212. http://geodesic.mathdoc.fr/item/ADM_2019_28_2_a5/

[1] M. Bestvina, “Local homology properties of boundaries of groups”, Michigan Math. J., 43:1 (1996), 123–139 | DOI | MR | Zbl

[2] M. Bestvina, G. Mess, “The boundary of negatively curved groups”, J. Amer. Math. Soc., 4:3 (1991), 469–481 | DOI | MR | Zbl

[3] R. Bieri, Homological dimension of discrete groups, Quinn Mary College, 191 pp. | MR

[4] Amer. Math. Soc. Translation, 1951:48 (1951), 3–6 | MR | MR

[5] K. Brown, Cohomology of groups, Springer, New York–Heidelberg–Berlin, 1982 | MR | Zbl

[6] G. Bredon, Sheaf Theory, Graduate Text in Mathematics, 170, Springer, New York–Heidelberg–Berlin, 1997 | DOI | MR | Zbl

[7] A. Dranishnikov, “On the virtual cohomological dimensions of Coxeter groups”, Proc. Amer. Math. Soc., 125:7 (1997), 1885–1891 | DOI | MR | Zbl

[8] A. Dranishnikov, “Boundaries of Coxeter groups and simplicial complexes with given links”, J. Pure Appl. Algebra, 137:2 (1999), 139–151 | DOI | MR | Zbl

[9] A. Dranishnikov, On topological complexity of hyperbolic groups, Preprint, arXiv: 1904.06720 | MR

[10] A. Dranishnikov, R. Sadykov, “The topological complexity of the free product”, Mathematische Zeitschrift, 293:1 (2019), 407–416 | DOI | MR | Zbl

[11] M. Farber, Invitation to topological robotics, Zurich Lectures in Advanced Mathematics, European Mathematical Society, Zürich, 2008 | MR | Zbl

[12] M. Farber, S. Mescher, “On the topological complexity of aspherical spaces”, Journal of Topology and Analysis, to appear | MR

[13] L. Fuchs, Infinite abelian groups, v. 1, Academic Press, 1970 | MR | Zbl

[14] L. S. Pontryagin, “Sur une hypothese fondamentale de la theorie de la dimension”, C. R. Acad. Sci. Paris, 190 (1930), 1105–1107