For the last thirty years the EHP sequence has been a major conceptual tool in the attempt to understand the homotopy groups of spheres. It is a collection of long exact sequences of homotopy groups induced by certain fibrations in which all three spaces are loop spaces of spheres. These fibrations are due originally to James, G. W. Whitehead, and Toda. The Freudenthal suspension theorem and th...

In [1], Miller, Ravenel and Wilson defined generalized beta elements in the E2-term of the Adams-Novikov spectral sequence converging to the stable homotopy groups of spheres, and in [5], Oka showed that the beta elements of the form βtp2/r for positive integers t and r survives to the stable homotopy groups at a prime p > 3, when r ≤ 2p − 2 and r ≤ 2p if t > 1. In this paper, we expand the con...

We study the Brunnian subgroups and the boundary Brunnian subgroups of the Artin braid groups. The general higher homotopy groups of the sphere are given by mirror symmetric elements in the quotient groups of the Artin braid groups modulo the boundary Brunnian braids, as well as given as a summand of the center of the quotient groups of Artin pure braid groups modulo boundary Brunnian braids. T...

We examine the “homotopy coniveau tower” for a general cohomology theory on smooth k-schemes, satisfying some natural axioms, and give a new proof that the layers of this tower for K-theory agree with motivic cohomology. We show how these constructions lead to a tower of functors on the Morel-Voevodsky stable homotopy category, and identify this stable homotopy coniveau tower with Voevodsky’s s...

Abstract Using techniques in motivic homotopy theory, especially the theorem of Gheorghe, second and third author on isomorphism between Adams spectral sequence for $C\tau $ C τ algebraic Novikov $BP_{*}$ B P ∗ , we com...

The homotopy perturbation method is a powerful device for solving a wide variety of problems arising in many scientific applications. In this paper, we investigate several integral equations by using T-stability of the Homotopy perturbation method investigates for solving integral equations. Some illustrative examples are presented to show that the Homotopy perturbation method is T-stable for s...