Abstract.Algebraic and geometrical techniques are used to study examples (new and previously conjectured) of «-dimensional simplicial complexes which cannot be topologically imbedded in Euclidean 2«-space, but each proper subcomplex of any of them can be imbedded in Euclidean 2«-space.
Examples are given showing the limitations of the homology of the deleted product in determining the imbeddability of simplicial complexes in a given Euclidean space. It is also proven that the only finite 1-complexes whose polyhedral deleted products are closed 2-manifolds are the two primitive skew curves of Kuratowski.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.