Relations between several Adams spectral sequences

On Relations between Adams Spectral Sequences, with an Application to the Stable Homotopy of a Moore Space

abutting to the stable homotopy of X. It has long been recognized that a map A +B of ring-spectra gives rise to information about the differentials in this spectral sequence. The main purpose of this paper is to prove a systematic theorem in this direction, and give some applications. To fix ideas, let p be a prime number, and take B to be the modp EilenbergMacLane spectrum H and A to be the Br...

Relations Between Several Parallel Computational Models

We investigate the relative computational power of parallel models with shared memory. Based on feasibility considerations present in the literature, we split these models into “lightweight” and “heavyweight,” and then find that the heavyweight class is strictly more powerful than the lightweight class, as expected. On the other hand, we contradict the long held belief that the heavyweight mode...

The Motivic Adams Spectral Sequence

We present some data on the cohomology of the motivic Steenrod algebra over an algebraically closed field of characteristic 0. Our results are based on computer calculations and a motivic version of the May spectral sequence. We discuss features of the associated Adams spectral sequence, and use these tools to give new proofs of some results in classical algebraic topology. We also consider a m...

An Adams Spectral Sequence Primer

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 can quickly become overwhelming if one starts with the generalized Adams spectral sequence. The classical Adams spectral sequence, in contrast, can be quickly set up and used to do some calculations which...

Relations between Sequences and Selection Properties