The 7-connected Cobordism Ring

THE 7 - CONNECTED COBORDISM RING AT p = 3

In this paper, we study the cobordism spectrum MOh8i at the prime 3. This spectrum is important because it is conjectured to play the role for elliptic cohomology that Spin cobordism plays for real K-theory. We show that the torsion is all killed by 3, and that the Adams-Novikov spectral sequence collapses after only 2 diierentials. Many of our methods apply more generally.

Cobordism Theory Using Steenrod Operations

In this paper I give new proofs of the structure theorems for the unoriented cobordism ring [12] and the complex cobordism ring [8, 131. The proofs are elementary in the sense that no mention of the Steenrod algebra or Adams spectral sequence is made. In fact, the only result from homotopy theory which is used in an essential way is the Serre finiteness theorem in order to know that the complex...

The 7 - Connected Cobordism

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 Oriented Cobordism Ring

We give an exposition of the computation of the oriented cobordism ring ΩSO ∗ using the Adam’s spectral sequence. Our proof follows Pengelley [15]. The unoriented and complex cobordism rings are also computed in a similar fashion.