let $p$ be a prime number greater than three. in this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(s)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm ext}_a^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{z}_p,mathbb{z}_p)$ up to nonzero scalar in the adams spectral sequence, where $ngeq m+2>5$, $0leq sext}_a^{s+2,q[(s+2)p...

This paper studies Kontsevich’s characteristic classes of smooth bundles with fiber a ‘singularly’ framed odd-dimensional homology sphere which are defined through his graph complex and configuration space integral. We will give a systematic construction of smooth bundles parametrized by trivalent graphs and will show that our smooth bundles are nontrivially detected by Kontsevich’s characteris...

Let $p$ be a prime number greater than three. In this paper, we prove the existence of a new family of homotopy elements in the stable homotopy groups of spheres $pi_{ast}(S)$ which is represented by $h_nh_mtilde{beta}_{s+2}in {rm Ext}_A^{s+4, q[p^n+p^m+(s+2)p+(s+1)]+s}(mathbb{Z}_p,mathbb{Z}_p)$ up to nonzero scalar in the Adams spectral sequence, where $ngeq m+2>5$, $0leq sExt}_A^{s+2,q[(s+2)p...

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...

We set up foundations of representation theory over S, the stable sphere, which is the “initial ring” of stable homotopy theory. In particular, we treat S-Lie algebras and their representations, characters, gln(S)-Verma modules and their duals, HarishChandra pairs and Zuckermann functors. As an application, we construct a Khovanov slk-stable homotopy type with a large prime hypothesis, which is...

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.