In a previous paper [5], the authors investigated extensively the Landweber-Araki Real cobordism spectrum MR ([1, 7]), and its stable summand at p = 2 called BPR. An Adams-like spectral sequence based on BPR was constructed, and homotopy groups of many spectra related to BPR were calculated. The goal of the present note is to begin investigating the question as to how BPR-theory contributes to ...

We show that one can construct the universal R-homology isomorphism K ~ E~X of Bousfield [1] by a transfinite iteration of an elementary homology correction map. This correction map is essentially the same as the one used classically to define Adams spectral sequence. This yields a topological characterization of the class of local spaces as the smallest s containing K(A, n)'s and closed under ...

We characterize the 2-line of the p-local Adams-Novikov spectral sequence in terms of modular forms satisfying a certain explicit congruence condition for primes p ≥ 5. We give a similar characterization of the 1-line, reinterpreting a computation of A. Baker. These results are then used to deduce that, for ` a prime which generates Zp , the spectrum Q(`) detects the α and β families in the sta...

In this paper, we study the cobordism spectrum MO〈8〉 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 differentials. Many of our methods apply more generally.

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.

The periodic lambda algebra is a co-Koszul complex of the Steenrod algebra whose homology gives the E2 term for the Adams spectral sequence. Its elements are closely related to periodic homotopy theory, and exhibit periodic properties. In this paper we discuss an algorithm to compute the homology of the periodic lambda algebra, and investigate the algebraic structure for the E2 page of the vn p...

We construct the centralizer resolution of the spectrum EhS 1 2 in the category of K(2)-local spectra at the prime 2. We use the associated tower of fibrations to realize the duality resolution to a tower of fibrations whose limit is the spectrum EhS 1 2 . We also compute the Adams-Novikov spectral sequence for the spectrum tmf without assuming the ring structure on the spectrum and compute π∗E...

The chromatic spectral sequence is introduced in [8] to compute the E2-term of the Adams-Novikov spectral sequence for computing the stable homotopy groups of spheres. The E1-term E s,t 1 (k) of the spectral sequence is an Ext group of BP∗BP -comodules. There are a sequence of Ext groups E 1 (n − s) for non-negative integers n with E s,t 1 (0) = E s,t 1 , and Bockstein spectral sequences comput...

Abstract As a step towards understanding the $$\mathrm {tmf}$$ tmf -based Adams spectral sequence, we compute K (1)-local homotopy of {tmf}\wedge \mathrm xmlns:mml="http://www.w3.org/1998/Math/MathML">tmf∧tmf , using small presen...