On Hawaiian homology groups

Abstract

In this paper, we introduce a kind of homology which we call Hawaiian homology to study and classify pointed topological spaces. The Hawaiian homology group has advantages of Hawaiian groups. Moreover, the first Hawaiian homology group is isomorphic to the abelianization of the first Hawaiian group for path-connected and locally path-connected topological spaces. Since Hawaiian homology has concrete elements and abelian structure, its calculations are more routine. Thus we use Hawaiian homology groups to compare Hawaiian groups, and then we obtain some information about Hawaiian groups of some wild topological spaces.