Type: Article
Publication Date: 1970-04-01
Citations: 32
DOI: https://doi.org/10.2140/pjm.1970.33.89
It is known that the fixed point property (f.p.p.) is not invariant under suspension and join in the category of simply connected polyhedra.In this paper we exhibit examples to show that f .p.p. is not invariant under suspension and join in the category of simply connected polyhedra satisfying the Shi condition and more strongly, in the category of simply connected compact manifolds.We also exhibit a simply connected polyhedron X such that the smash product X A X fails to have f.p.p. if one choice of base point is used to form X A X, while X A X has f .p.p. using another choice of base point.In the last section we prove that f .p.p. is invariant under Cartesian products in very special circumstances.