An elementary construction of Anick's fibration

TL;DR

This paper presents a new, more conceptual construction of Anick's fibration for odd primes, extending its validity to p=3 and exploring properties of the constructed space.

Contribution

The authors provide a simplified, more conceptual construction of Anick's fibration applicable for p=3 and p>=5, improving upon previous complex methods.

Findings

Construction valid for p=3 and p>=5

Established properties of the space T

Simplified approach to Anick's fibration

Abstract

Cohen, Moore, and Neisendorfer's work on the odd primary homotopy theory of spheres and Moore spaces, as well as the first author's work on the secondary suspension, predicted the existence of a p-local fibration S^2n-1 --> T --> \Omega S^2n+1 whose connecting map is degree p^r. In a long and complex monograph, Anick constructed such a fibration for p>= 5 and r>= 1. Using new methods we give a much more conceptual construction which is also valid for p=3 and r>= 1. We go on to establish several properties of the space T.