Decompositions involving Anick's spaces

TL;DR

This paper presents an elementary construction of Anick's spaces, decomposes their fundamental fibration, and explores their properties to facilitate understanding of maps and universal characteristics.

Contribution

It introduces a new elementary construction of Anick's spaces and decomposes their fundamental fibration to analyze their properties.

Findings

Decomposition of the fundamental fibration of Anick's spaces

Enhanced understanding of maps from Anick's spaces

Insights into the universal properties of Anick's spaces

Abstract

Recently Stephen Theriault and I found an elementary construction of Anick's spaces and proved their main properties(arXiv:0710.1024).In this work the fundamental fibration is decomposed. This is useful in studying maps out of Anick's spaces and will be needed in order to determine it's universal properties.