Non-trivial Odd Dimensional Equivariant Cohomology of Torus Orbits of Generic Points in $gr(2,k)$

Abstract

Examples of odd equivariant cohomology exist in the literature, but they are generally in degree one and used to show only that odd equivariant cohomology can exist. This paper produces a family of toric varieties which have non trivial odd equivariant cohomology which arise as torus orbits of generic points in the grassmannian in many odd degrees. We then show that is it is possible to compute the equivariant cohomology explicitly with \mathbb{Q}-coefficients in H^3_T for small examples.