Tame Z²-actions on Eⁿ

Paul Frazier Duvall, Jr. and Jim Maxwell

Vol. 49 (1973), No. 2, 349–355

DOI: 10.2140/pjm.1973.49.349

Abstract

Let ℋ(Eⁿ) denote the group of homeomorphisms of euclidean n-space, and G a subgroup isomorphic to Z ⊕Z.G is said to be a Z²-action on Eⁿ and two such actions ale said to be equivalent if they are conjugate in ℋ(Eⁿ). In §2, the notion of a tame Z²-action is introduced and for n ≧ 5 tame Z²-actions are shown to be classified by π₁(SO_n−2)≅Z₂. In §3, tameness is shown to be inherited by a subaction of a tame Z²-action and an example of a nontame Z²-action with tame subactions is given.

Mathematical Subject Classification

Primary: 57E30

Milestones

Received: 3 August 1972

Published: 1 December 1973