Geodesic
The integral cohomology algebras of ordered configuration spaces of spheres
Documenta mathematica, Tome 5 (2000), pp. 115-139
Cet article a éte moissonné depuis la source EMS Press

Voir la notice de l'article

We compute the cohomology algebras of spaces of ordered point configurations on spheres, F(Sk,n), with integer coefficients. For k=2 we describe a product structure that splits F(S2,n) into well-studied spaces. For k>2 we analyze the spectral sequence associated to a classical fiber map on the configuration space. In both cases we obtain a complete and explicit description of the integer cohomology algebra of F(Sk,n) in terms of generators, relations and linear bases. There is 2-torsion occuring if and only if k is even. We explain this phenomenon by relating it to the Euler classes of spheres. Our rather classical methods uncover combinatorial structures at the core of the problem.
DOI : 10.4171/dm/76
Classification : 52C35, 55M99, 55R20, 57N65
Mots-clés : spheres, ordered configuration spaces, subspace arrangements, integral cohomology algebra, fibration, Serre spectral sequence 
@article{10_4171_dm_76,
     author = {Eva Maria Feichtner and G\"unter M. Ziegler},
     title = {The integral cohomology algebras of ordered configuration spaces of spheres},
     journal = {Documenta mathematica},
     pages = {115--139},
     year = {2000},
     volume = {5},
     doi = {10.4171/dm/76},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/76/}
}
TY  - JOUR
AU  - Eva Maria Feichtner
AU  - Günter M. Ziegler
TI  - The integral cohomology algebras of ordered configuration spaces of spheres
JO  - Documenta mathematica
PY  - 2000
SP  - 115
EP  - 139
VL  - 5
UR  - http://geodesic.mathdoc.fr/articles/10.4171/dm/76/
DO  - 10.4171/dm/76
ID  - 10_4171_dm_76
ER  - 
%0 Journal Article
%A Eva Maria Feichtner
%A Günter M. Ziegler
%T The integral cohomology algebras of ordered configuration spaces of spheres
%J Documenta mathematica
%D 2000
%P 115-139
%V 5
%U http://geodesic.mathdoc.fr/articles/10.4171/dm/76/
%R 10.4171/dm/76
%F 10_4171_dm_76
Eva Maria Feichtner; Günter M. Ziegler. The integral cohomology algebras of ordered configuration spaces of spheres. Documenta mathematica, Tome 5 (2000), pp. 115-139. doi: 10.4171/dm/76

Cité par Sources :