Vol. 89, No. 2, 1980

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

Sushil Jajodia

Vol. 89 (1980), No. 2, 301–311
Abstract

Let Ξ be a one-relator group with presentation = (x1,,xn : Rp) 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 (p,q) for Ξ from the cellular model C() of the presentation by attaching a 3-cell via the attaching map Rq 1, which generates the ideal ZΞ(R 1) π2(C()). 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
Authors
Sushil Jajodia