Generalized homology theories

Generalized Homology Theories

The Mayer-vietoris Sequence for Generalized Homology Theories

Generalized Local Homology Modules of Complexes

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

Equivariant Stratifold Homology Theories

We define equivariant homology theories using bordism of stratifolds with a G-action, where G is a discrete group. Stratifolds are a generalization of smooth manifolds which were introduced by Kreck [Kre02]. He defines homology theories using bordism of suitable stratifolds. We develop the equivariant generalization of these ideas.

Interpolation Categories for Homology Theories

For a homological functor from a triangulated category to an abelian category satisfying some technical assumptions we construct a tower of interpolation categories. These are categories over which the functor factorizes and which capture more and more information according to the injective dimension of the images of the functor. The categories are obtained by using truncated versions of resolu...