On the homotopy of \(Q(3)\) and \(Q(5)\) at the prime 2 (Q341746)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On the homotopy of \(Q(3)\) and \(Q(5)\) at the prime 2 |
scientific article; zbMATH DE number 6653748
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the homotopy of \(Q(3)\) and \(Q(5)\) at the prime 2 |
scientific article; zbMATH DE number 6653748 |
Statements
On the homotopy of \(Q(3)\) and \(Q(5)\) at the prime 2 (English)
0 references
17 November 2016
0 references
stable homotopy group
0 references
\(K(2)\)-local sphere
0 references
topological modular forms
0 references
\(v_n\)-periodicity
0 references
elliptic curve
0 references
0.87551534
0 references
0.8693778
0 references
0.8591038
0 references
0.8542024
0 references
0.84608245
0 references
0.84465176
0 references
The article under review belongs to the subject of computational stable homotopy theory. One of the longstanding goals of this subject is to understand the \(K(2)\)-local sphere. (The \(K(1)\)-local sphere is already well-understood.)NEWLINENEWLINEThe authors do not directly study the \(K(2)\)-local sphere, but rather some approximations \(Q(3)\) and \(Q(5)\). They carry out detailed calculations of the homotopy of these approximations. All of this hard work sheds light on the behavior of the \(K(2)\)-local sphere.NEWLINENEWLINEThis work builds on earlier computational work of Mahowald, Rezk, and others.NEWLINENEWLINEThe article focuses only on the hardest prime \(p = 2\).
0 references
