In [1] Adams constructed a non-nilpotent map v 1 : Σ S/2 −→ S/2. Using iterates of this map one constructs infinite families of elements in the stable homotopy groups of spheres, the v1-periodic elements of order 2. In this paper we work motivically over C and construct a nonnilpotent self map w 1 : Σ S/η −→ S/η. We then construct some infinite families of elements in the homotopy of the motivi...

Let p be a prime number greater than three. In the p-component of stable homotopy groups of spheres, Oka constructed a beta family from a v2-periodic map on a four cell complex. In this paper, we construct another beta family in the groups at a prime p greater than five from a v2-periodic map on a eight cell complex.

We revisit Freyd’s generating hypothesis in stable homotopy theory. We derive new equivalent forms of the generating hypothesis and some new consequences of it. A surprising one is that I, the Brown-Comenetz dual of the sphere and the source of many counterexamples in stable homotopy, is the cofiber of a self map of a wedge of spheres. We also show that a consequence of the generating hypothesi...

The Moore spectrum Mp(i) is the cofiber of pi map on sphere spectrum. For a fixed p and n, we find lower bound i for which guaranteed to be n-fold associative. This depends stable homotopy groups spheres.

We prove that for n ≥ 1 and q > 0 the (oriented) cobordism group of fold maps of (oriented) (n + q)-dimensional manifolds into R contains the direct sum of ⌊(q + 1)/2⌋ copies of the (n − 1)th stable homotopy group of spheres as a direct summand. We also prove that for k ≥ 1 and q = 2k − 1 the cobordism group of fold maps of unoriented (n+ q)-dimensional manifolds into R also contains the nth st...

We study the image of a transfer homomorphism in the stable homotopy groups of spheres. Actually, we show that an element of order 8 in the 18 dimensional stable stem is in the image of a double transfer homomorphism, which reproves a result due to P J Eccles that the element is represented by a framed hypersurface. Also, we determine the image of the transfer homomorphism in the 16 dimensional...

We introduce the (general) homotopy groups of spheres as link invariants for Brunnian-type links through the investigations on the intersection subgroup of the normal closures of the meridians of strongly nonsplittable links. The homotopy groups measure the difference between the intersection subgroup and symmetric commutator subgroup of the normal closures of the meridians and give the invaria...