Digital pseudomanifolds, digital weakmanifolds and Jordan-Brouwer separation theorem

In this paper we introduce the new notion of n-pseudomanifold and n-weakmanifold in an (n+1)-digital image using (2(n+1),3(n+1)-1)-adjacency. For these classes, we prove the digital version of the Jordan-Brouwer separation theorem. To accomplish this objective, we construct a polyhedral representation of the (n+1)-digital image based on a cubical complex decomposition which enables us to translate some results from polyhedral topology into the digital space. Our main result extends the class of "thin" objects that are defined locally and verifying the Jordan-Brouwer separation theorem.