Homotopy classification of lens spaces for one-relator groups with torsion

Sushil Jajodia

Vol. 89 (1980), No. 2, 301–311

DOI: 10.2140/pjm.1980.89.301

Abstract

Let Ξ be a one-relator group with presentation ℛ = (x₁,⋯,x_n : R^p) where R is not a proper power and p ≧ 2. Then given any integer q, relatively prime to p, we can construct the Lens space ℒ(p,q) for Ξ from the cellular model C(ℛ) of the presentation ℛ by attaching a 3-cell via the attaching map R^q − 1, which generates the ideal ZΞ(R − 1) ≈ π₂(C(ℛ)). In this paper we classify these Lens spaces up to homotopy type. We also discuss the non-cancellation aspect of these Lens spaces.

Mathematical Subject Classification 2000

Primary: 55P15

Milestones

Received: 19 July 1978

Revised: 6 July 1979

Published: 1 August 1980