The equivariant Orlik-Solomon algebra
| dc.creator | Proudfoot, Nicholas J. | |
| dc.date | 2003-06-02 | |
| dc.date | 2004-08-03 | |
| dc.date.accessioned | 2026-07-07T04:58:27Z | |
| dc.date.available | 2026-07-07T04:58:27Z | |
| dc.description | Given a real arrangement $A$, the complement $M(A)$ of the complexification of $A$ admits an action of $\mathbb{Z}_2$ by complex conjugation. We define the equivariant Orlik-Solomon algebra of $A$ to be the $\mathbb{Z}_2$-equivariant cohomology ring of $M(A)$ with coefficients in $\mathbb{Z}_2$. We give a combinatorial presentation of this ring, and interpret it as a deformation of the ordinary Orlik-Solomon algebra into the Varchenko-Gel'fand ring of locally constant $\mattbb{Z}_2$-valued functions on the complement $C(A)$ of $A$ in $\mathbb{R}^n$. We also show that the $\mathbb{Z}_2$-equivariant homotopy type of $M(A)$ is determined by the oriented matroid of $A$. As an application, we give two examples of pairs of arrangements $A$ and $A'$ such that $M(A)$ and $M(A')$ have the same nonequivariant homotopy type, but are distinguished by the equivariant Orlik-Solomon algebra. | |
| dc.description | 9 pages, 2 figures. Revised exposotion, corrections to examples | |
| dc.identifier | https://arxiv.org/abs/math/0306013 | |
| dc.identifier | http://arxiv.org/abs/math/0306013 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67641 | |
| dc.subject | Combinatorics | |
| dc.subject | Algebraic Topology | |
| dc.subject | Rings and Algebras | |
| dc.subject | 52C35 | |
| dc.title | The equivariant Orlik-Solomon algebra | |
| dc.type | text |