On β-elements in the 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...

ROOTS OF UNITY AND THE ADAMS-NOVIKOV SPECTRAL SEQUENCE FOR FORMAL yl-MODULES

The cohomology of a Hopf algebroid related to the Adams-Novikov spectral sequence for formal ,4-modules is studied in the special case in which A is the ring of integers in the field obtained by adjoining pth roots of unity to Qp , the p-adic numbers. Information about these cohomology groups is used to give new proofs of results about the E2 term of the Adams spectral sequence based on 2-local...