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.

This paper contains a complete computation of the homotopy ring of the spectrum of topological modular forms constructed by Hopkins and Miller. The computation is done away from 6, and at the (interesting) primes 2 and 3 separately, and in each of the latter two cases, a sequence of algebraic Bockstein spectral sequences is used to compute the E2 term of the elliptic Adams-Novikov spectral sequ...

Let n be any positive integer and p any prime. Also, let X be any spectrum and let K(n) denote the nth Morava K-theory spectrum. Then we construct a descent spectral sequence with abutment π∗(LK(n)(X)) and E2-term equal to the continuous cohomology of Gn, the extended Morava stabilizer group, with coefficients in a certain discrete Gn-module that is built from various homotopy fixed point spect...

Article history: Received 20 November 2014 Received in revised form 17 February 2015 Communicated by C.A. Weibel MSC: 14F42; 55T15; 55S10 We compute the h1-localized cohomology of the motivic Steenrod algebra over C. This serves as the input to an Adams spectral sequence that computes the motivic stable homotopy groups of the η-local motivic sphere. We compute some of the Adams differentials, a...

The $E_2$ term of the Adams spectral sequence may be identified with certain derived functors, and this also holds for a number other sequences. Our goal is to show how higher terms such sequences are determined by truncations relative defined in simplicial functors called mapping algebras

IN HIS WORK on complex cobordism [ 181 Novikov introduced a spectral sequence converging to the stable homotopy of a space, depending only on the complex cobordism of the space as a module over the ring of primary complex cobordism operations. This spectral sequence can be localized at a prime p and one can work, as Novikov did, with the smaller theory, BP*( ), known as Brown-Peterson cohomolog...

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...

We investigate the E2-term of Adams spectral sequence based on elliptic homology. The main results describe this E2-term from a ‘chromatic’ perspective. At a prime p > 3, the Bousfield class of Ell is the same as that of K(0)∨K(1)∨ K(2). Using delicate facts due to Katz (which also play a major rôle in work on the structure Ell∗Ell by Clarke & Johnson, the author and Laures) as well as our desc...

in this paper, a new spectral-iterative method is employed to give approximate solutions of fractional logistic differential equation. this approach is based on combination of two different methods, i.e. the iterative method cite{35} and the spectral method. the method reduces the differential equation to systems of linear algebraic equations and then the resulting systems are solved by a numer...