Some calculations in the unstable Adams-Novikov spectral sequence

The Adams-novikov Spectral Sequence for the Spheres

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...

BP -Theory and the Adams–Novikov Spectral Sequence

The Adams-Novikov Spectral Sequence and the Homotopy Groups of Spheres

These are notes for a five lecture series intended to uncover large-scale phenomena in the homotopy groups of spheres using the Adams-Novikov Spectral Sequence. The lectures were given in Strasbourg, May 7–11, 2007.

THE Ext-TERM OF THE REAL-ORIENTED ADAMS-NOVIKOV SPECTRAL SEQUENCE

The spectral sequence (1) was introduced in [9] and [8]. Here, BPR is the Realoriented Brown-Peterson spectrum, which was constructed from Landweber’s Real cobordism spectrum MR [10] by Araki [2]. These are Z/2-equivariant spectra, indexed on RO(Z/2). The subscript ⋆ refers to the RO(Z/2)-indexing, i. e. all (bi)degrees k + lα, k, l ∈ Z, where α is the sign representation of Z/2. Thus, the spec...

On the unstable Adams spectral sequence for SO and U , and splittings of unstable Ext groups ∗

Let U denote the category of unstable modules over the mod 2 Steenrod algebra A, and let Ext(−) = ExtsU(−,ΣZ2). Let M∞ = H̃∗(ΣCP∞ + ) denote the unstable A-module with nonzero classes xi such that i is odd and positive, and Sqx2k+1 = ( k j ) x2(j+k)+1. Then H∗(U) ≈ U(M∞), where the left side is the mod 2 cohomology of the infinite unitary group, and the right side the free unstable A-algebra gen...