Vol. 53, No. 2, 1974

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Torus group actions on simply connected manifolds

Soon-Kyu Kim, Dennis McGavran and Jingyal Pak

Vol. 53 (1974), No. 2, 435–444
Abstract

In this paper it is shown that effective torus Tn-actions on simply connected closed (n + 2)-manifolds Mn+2 for all n 1 exist, and a complete orbit structure is given. It turns out that all maximal isotropy subgroups must generate the whole group Tn. The cross-sectioning theorem for the orbit map π : M M = Mn+2∕Tn is given, and as its application an equivariant classification theorem is obtained.

It is also shown that free torus Tn-actions on simply connected closed (n + 4)-manifolds for all n 1 exist.

Mathematical Subject Classification
Primary: 57E15
Milestones
Received: 5 April 1973
Revised: 15 February 1974
Published: 1 August 1974
Authors
Soon-Kyu Kim
Dennis McGavran
Jingyal Pak