Pattern-equivariant homology
Pattern-equivariant homology
Pattern-equivariant (PE) cohomology is a well-established tool with which to interpret the \v{C}ech cohomology groups of a tiling space in a highly geometric way. In this paper we consider homology groups of PE infinite chains. We establish Poincar\'{e} duality between the PE cohomology and PE homology. The Penrose kite and …