1/2-Homogeneous suspensions

A space is said to be 1 2 -homogeneous provided there are exactly two orbits for the action of the group of homeomorphisms of the space onto itself. Certain conditions on a compactum X are known under which the cone over X is 1 2 -homogeneous (Nadler Jr. and Pellicer-Covarrubias (2007) [16]). In this paper we investigate 1 2 -homogeneity in suspensions of compact metric spaces; namely, we determine necessary and sufficient conditions under which the suspension of a continuum X is 1 2 -homogeneous, among certain classes of continua. This paper gives a partial answer to a question posed by S.B. Nadler Jr. (2007) in [14, p. 342].