On Hawaiian homology groups

Year 2024, Early Access, 1 - 20

Professor Dr. , Hanıeh Mırebrahımı , Ameneh Babaee

https://doi.org/10.15672/hujms.1298585

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.

Keywords

awaiian group, singular homology, archipelago space, Higmann-complete group, cotorsion group

Supporting Institution

Ferdowsi University of Mashhad

Project Number

2/57128

References

• [1] J.F. Adamas, Stable homotopy and generalised homology, The university of Chicago press, Chicago, 1974