Add to ORKGWe construct certain unstable higher-order homotopy operations indexed by the simplex categories of $\Delta^{n}$ for ${n\geq 2}$ and prove that all elements in the homotopy groups of a wedge of spheres are generated under such operations by Whitehead products and the group structure. This provides a stronger unstable analogue of Cohen's theorem on the decomposition of stable homotopy.Comment: The articles 'The higher structure of unstable homotopy groups' and 'Note on Toda brackets' subsume the submission 1810-0600
In this thesis, we study the fibre of the $p^\text{th}$ power map on loop spaces of spheres with a v...
In this thesis, we study the fibre of the $p^\text{th}$ power map on loop spaces of spheres with a v...
The purpose of this thesis is to study the higher Hochschild homology of some rational algebras. We ...
We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new co...
We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and us...
We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and us...
We study several different notions of algebraicity in use in stable homotopy theory and prove implic...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.Cataloged fro...
In this paper, we propose a new method to the homotopy classification of maps between $(n-1)$-connec...
We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1 \tim...
We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typica...
We study the structure of the $RO(G)$-graded homotopy Mackey functors of any Eilenberg-MacLane spect...
In recent years, spectral algebra or stable homotopical algebra over structured ring spectra has bec...
For the last thirty years the EHP sequence has been a major conceptual tool in the attempt to unders...
1. Brief introduction to a lengthy subject Determining the stable homotopy groups of spheres has bee...
In this thesis, we study the fibre of the $p^\text{th}$ power map on loop spaces of spheres with a v...
In this thesis, we study the fibre of the $p^\text{th}$ power map on loop spaces of spheres with a v...
The purpose of this thesis is to study the higher Hochschild homology of some rational algebras. We ...
We discuss the current state of knowledge of stable homotopy groups of spheres. We describe a new co...
We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and us...
We give a refinement of the stable Snaith splitting of the double loop space of a Moore space and us...
We study several different notions of algebraicity in use in stable homotopy theory and prove implic...
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2015.Cataloged fro...
In this paper, we propose a new method to the homotopy classification of maps between $(n-1)$-connec...
We study the infinite generation in the homotopy groups of the group of diffeomorphisms of $S^1 \tim...
We study the homotopy of the connected sum of a manifold with a projective space, viewed as a typica...
We study the structure of the $RO(G)$-graded homotopy Mackey functors of any Eilenberg-MacLane spect...
In recent years, spectral algebra or stable homotopical algebra over structured ring spectra has bec...
For the last thirty years the EHP sequence has been a major conceptual tool in the attempt to unders...
1. Brief introduction to a lengthy subject Determining the stable homotopy groups of spheres has bee...
In this thesis, we study the fibre of the $p^\text{th}$ power map on loop spaces of spheres with a v...
In this thesis, we study the fibre of the $p^\text{th}$ power map on loop spaces of spheres with a v...
The purpose of this thesis is to study the higher Hochschild homology of some rational algebras. We ...