The topology of tile invariants (Q491335)

In this paper, the author uses techniques in the topology of 2-complexes to recast some tools that have arisen in the study of planar tiling questions. With spherical pictures, the author shows that the tile counting group associated to a set \(T\) of tiles and a set of regions tileable by \(T\) is isomorphic to a quotient of the second homology group of a 2-complex built from \(T\). In this topological setting, the author derives some well-known tile invariants, one of which he applies to the solution of a tiling question involving modified rectangles.