Homotopy dimension of some orbit spaces

Vo Thanh Liem

Vol. 92 (1981), No. 2, 357–363

DOI: 10.2140/pjm.1981.92.357

Abstract

The homotopy dimension of a compact absolute neighborhood retract space X is defined to be the least dimension among all the finite CW-complexes which have the same homotopy type of X. We show that actions of finite groups or actions of tori (with finite orbit types) on a finite-dimensional compact absolute neighborhood retract X do not raise homotopy dimension if the homotopy dimension of X is not two.

Mathematical Subject Classification 2000

Primary: 57S25

Secondary: 57N20, 57S17

Milestones

Received: 30 November 1979

Published: 1 February 1981