Mod 2 cohomology ring of a kind of orbit configuration space

Abstract

In this paper we caculate mod 2 cohomology ring of $F_{{\mathbb{Z}}_2^m}({\mathbb{R}}^m,n)$ , which is local representation of orbit congfiguration spaces over small covers. We construct a differntial graded algebra, and there is a ring isomorphism between its mod 2 cohomology ring and $H^{\ast }(F_{{\mathbb{Z}}_2^m}({\mathbb{R}}^m,n),{\mathbb{Z}}_2)$. This idea can also be applied to calculate mod 2 cohomology ring of complement space of real arrangements.

8 pages