A loop space whose homology has torsion of all orders

David Jay Anick

Vol. 123 (1986), No. 2, 257–262

DOI: 10.2140/pjm.1986.123.257

Abstract

In this note we will construct a simply-connected finite CW complex X of dimension four with the following property. For each positive integer m, there is an element ω_m of order m in π_m+1(ΩX) whose Hurewicz image h(ω_m) ∈ H_m+1(ΩX) also has order m. Such a space illustrates how intricate loop space homology can be even for relatively simple spaces.

Mathematical Subject Classification 2000

Primary: 55P35

Secondary: 55Q15

Milestones

Received: 26 February 1985

Published: 1 June 1986