Vol. 71, No. 2, 1977

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Tn-actions on simply connected (n + 2)-manifolds

Dennis McGavran

Vol. 71 (1977), No. 2, 487–497
Abstract

In this paper we show that, for each n 2, there is a unique, closed, compact, connected, simply connected (n + 2)-manifold, Mn+2, admitting an action of Tn satisfying the following condition: there are exactly n T1-stability groups T1,,Tn with each F(Ti,Mn+2) connected. In this case we have TnT1 × × Tn. Any other action (Tn,Mn+2), Mn+2 simply connected, can be obtained from an action (Tn,Mn+2) by equivariantly replacing copies of D4 × Tn2 with copies of S3 × D2 × Tn3. As an application, we classify all actions of Tn on simply connected (n + 2)-manifolds for n = 3,4.

Mathematical Subject Classification
Primary: 57E25, 57E25
Milestones
Received: 20 May 1976
Published: 1 August 1977
Authors
Dennis McGavran