The Adams–Novikov spectral sequence and Voevodsky’s slice tower

On the slice spectral sequence

We introduce a variant of the slice spectral sequence which uses only regular slice cells, and state the precise relationship between the two spectral sequences. We analyze how the slice filtration of an equivariant spectrum that is concentrated over a normal subgroup is related to the slice filtration of its geometric fixed points, and use this to prove a conjecture of Hill on the slice filtra...

Convergence of Voevodsky’s Slice Tower

We consider Voevodsky’s slice tower for a finite spectrum E in the motivic stable homotopy category over a perfect field k. In case k has finite cohomological dimension (in characteristic two, we also require that k is infinite), we show that the slice tower converges, in that the induced filtration on the bi-graded homotopy sheaves Πa,bfnE is finite, exhaustive and separated at each stalk. Thi...

The Goodwillie tower and the EHP sequence

We study the interaction between the EHP sequence and the Goodwillie tower of the identity evaluated at spheres at the prime 2. Both give rise to spectral sequences (the EHP spectral sequence and the Goodwillie spectral sequence, respectively) which compute the unstable homotopy groups of spheres. We relate the Goodwillie filtration to the P map, and the Goodwillie differentials to the H map. F...

The Slice Spectral Sequence of Mackey Functors for the C4 Analog of Real K-theory

The purpose of this paper is to describe the slice spectral sequence of a 32-periodic C4-spectrum KH (to be defined below in §6, specifically Definition 6.3) related to the C4 norm (defined in [HHRa, §2.2.3]) MU ((C4)) = N4 C2MUR of the real cobordism spectrum MUR. Part of this spectral sequence is illustrated in an unpublished poster produced in late 2008 and shown in Figure 1. It shows the sp...

THE SLICE SPECTRAL SEQUENCE FOR RO(Cpn)-GRADED SUSPENSIONS OF HZ I