The equivariant cobordism category

Equivariant Algebraic Cobordism

We construct an equivariant algebraic cobordism theory for schemes with an action by a linear algebraic group over a field of characteristic zero.

Equivariant cobordism for torus actions

We study the equivariant cobordism groups for the action of a split torus T on varieties over a field k of characteristic zero. We show that for T acting on a variety X , there is an isomorphism ΩT ∗ (X) ⊗Ω∗(BT ) L ∼= −→ Ω∗(X). As applications, we show that for a connected linear algebraic group G acting on a k-variety X , the forgetful map ΩG ∗ (X) → Ω∗(X) is surjective with rational coefficie...

The Homotopy Type of the Cobordism Category

The Equivariant Complex Cobordism Ring of a Finite Abelian Group

We compute the equivariant (stable) complex cobordism ring (MUG)∗ for finite abelian groups G.

Equivariant Cw-complexes and the Orbit Category

We give a general framework for studying G-CW complexes via the orbit category. As an application we show that the symmetric group G = S5 admits a finite G-CW complex X homotopy equivalent to a sphere, with cyclic isotropy subgroups.