Recently Hopkins and Mahowald constructed a new 2-primary ring spectrum eo2, satisfying H (eo2) â‰ˆ A//A2. We use eo2 to obtain new results regarding nonimmersions of real projective spaces inâ€¦ (More)

Let Trk : F2 âŠ— GLk PHi(BVk) â†’ Ext A (F2, F2) be the algebraic transfer, which is defined by W. Singer as an algebraic version of the geometrical transfer trk : Ï€ S âˆ— ((BVk)+) â†’ Ï€S âˆ— (S0). It has beenâ€¦ (More)

We analyze in homological terms the homotopy fixed point spectrum of a T-equivariant commutative S -algebra R . There is a homological homotopy fixed point spectral sequence with E s,t = H âˆ’s gp (T;â€¦ (More)

Let ko be the real connective K-theory spectrum. We compute koâˆ—BG and koâˆ—BG for groups G whose Sylow 2-subgroup is quaternion of order 8. Using this we compute the coefficients t(ko)âˆ— of the G fixedâ€¦ (More)

The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partialâ€¦ (More)

We show how the root invariant of a product depends upon the product of the root invariants, give some examples of the equivariant definition of the root invariant, and verify a weakened form of theâ€¦ (More)

Greenlees thanks the University of She eld for URF grant number RSG/339. The large commutative diagrams in this article were typeset using Paul Taylor's diagram package. We give a brief exposition ofâ€¦ (More)

My aim with these notes is to quickly get the student started with the Adams spectral sequence. To see its power requires that some concrete calculations be done. However, the algebra required canâ€¦ (More)