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We show that the class of p-complete connective spectra with finitely presented cohomology over the Steenrod algebra admits a duality theory related to Brown-Comenetz duality. This construction also produces a full-plane version of the classical Adams spectral sequence for such spectra, which converges to the homotopy groups of a “finite” localization.

The Adams spectral sequence was invented by J.F.Adams [1] almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive ...

The Adams spectral sequence was invented by J.F.Adams [1] almost fifty years ago for calculations of stable homotopy groups of topological spaces and in particular of spheres. The calculation of differentials of this spectral sequence is one of the most difficult problem of Algebraic Topology. Here we consider an approach to solve this problem in the case of Z/2 coefficients and find inductive ...

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 partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η...

This paper proves that, for any generator x ∈ Ext A (Zp, Zp), if (1L ∧ i)∗φ∗(x) ∈ Ext A (H ∗L ∧ M,Zp) is a permanent cycle in the Adams spectral sequence (ASS), then h0x ∈ Ext A (Zp, Zp) also is a permenent cycle in the ASS. As an application, the paper obtains that h0hnhm ∈ Ext3,pnq+pmq+q A (Zp, Zp) is a permanent cycle in the ASS and it converges to elements of order p in the stable homotopy ...

The Adams spectral sequence has been an important tool in research on the stable homotopy of the spheres. In this note we outline new information about a variant of the Adams sequence which was introduced by Novikov [7]. We develop simplified techniques of computation which allow us to discover vanishing lines and periodicity near the edge of the E2-term, interesting elements in E^'*, and a cou...