The v1-periodic unstable 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...

A Novice's Guide to the Ad~ms-novikov Spectral Sequence

Ever since its introduction by J. F. Adams [8] in 1958, the spectral sequence that bears his name has been a source of fascination to homotopy theorists. By glancing at a table of its structure in low dimensions (such have been published in [7], [i0] and [27]; one can also be found in ~2) one sees not only the values of but the structural relations among the corresponding stable homotopy groups...

BP -Theory and the Adams–Novikov Spectral Sequence

3-PRIMARY v1-PERIODIC HOMOTOPY GROUPS OF E7

In this paper we compute the 3-primary v1-periodic homotopy groups of the exceptional Lie group E7. This represents the next stage in the author’s goal of calculating the v1-periodic homotopy groups of all compact simple Lie groups (at least when localized at an odd prime). Most of the work goes into calculating the unstable Novikov spectral sequence of ΩE7/Sp(2). Showing that this spectral seq...

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...