TY - JOUR
T1 - The integral cohomology of configuration spaces of pairs of points in real projective spaces
AU - Domínguez, Carlos
AU - González, Jesús
AU - Landweber, Peter
N1 - Funding Information:
The first author was supported by Conacyt Ph.D. scholarship number 162645. was partially supported by CONACYT Research Grant number 102783.
PY - 2013/11
Y1 - 2013/11
N2 - We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8 (in the case of unordered configurations, thus has only 2- and 4-torsion) or of the elementary abelian 2-group of rank 2 (in the case of ordered configurations, thus has only 2-torsion). As an application, we complete the computation of the symmetric topological complexity of real projective spaces P2i+8 with i ≤ 0 and 0 ≤δ ≤ 2.
AB - We compute the integral cohomology ring of configuration spaces of two points on a given real projective space. Apart from an integral class, the resulting ring is a quotient of the known integral cohomology of the dihedral group of order 8 (in the case of unordered configurations, thus has only 2- and 4-torsion) or of the elementary abelian 2-group of rank 2 (in the case of ordered configurations, thus has only 2-torsion). As an application, we complete the computation of the symmetric topological complexity of real projective spaces P2i+8 with i ≤ 0 and 0 ≤δ ≤ 2.
KW - 2-point configurations of real projective spaces
KW - Bockstein spectral sequence
KW - Dihedral group of order 8
KW - Euclidean embedding dimension
KW - Symmetric topological complexity
UR - http://www.scopus.com/inward/record.url?scp=84892189170&partnerID=8YFLogxK
U2 - 10.1515/FORM.2011.145
DO - 10.1515/FORM.2011.145
M3 - Artículo
AN - SCOPUS:84892189170
SN - 0933-7741
VL - 25
SP - 1217
EP - 1248
JO - Forum Mathematicum
JF - Forum Mathematicum
IS - 6
ER -