2-Primary Anick Fibrations

TL;DR

This paper proves Cohen's conjecture for r>=3, establishing the existence of certain spaces with specific homotopy fibration properties related to Anick fibrations.

Contribution

It confirms Cohen's conjecture for r≥3 and provides new preliminary results relevant to homotopy theory and Anick fibrations.

Findings

Confirmed Cohen's conjecture for r≥3

Constructed spaces T^{2n+1}(2^r) with specified homotopy properties

Developed preliminary results of independent interest

Abstract

Cohen conjectured that for r>=2 there is a space T^2n+1(2^r) and a homotopy fibration sequence Loop^2 S^2n+1 --> S^2n-1 --> T^2n+1(2^r) --> Loop S^2n+1 with the property that the left map composed with the double suspension, Loop^2 S^2n+1 --> S^2n-1 --> Loop^2 S^2n+1, is homotopic to the 2^r-power map. We positively resolve this conjecture when r>=3. Several preliminary results are also proved which are of interest in their own right.