Generalized Homology Groups

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 ...

PRECOMPACT TOPOLOGICAL GENERALIZED GROUPS

In this paper, we introduce and study the notion of precompacttopological generalized groups and some new results are given.

Generalized Homology Theories

Groups with Infinite Homology

A group is said to be acyclic if its reduced homology vanishes. Many interesting classes of groups have been discovered having this property ([2] is a useful survey). This is an indication that the reduced homology carries limited information. Here we obtain information about H̃(G) for a class of groups G that includes all locally finite groups and all soluble groups of finite rank. We show that...

Homology of jet groups

In this paper we compute the second homology of the discrete jet groups. Let R be the additive group of real numbers and R the multiplicative group of positive reals. The n jet group Jn = {rx+a2x + · · ·+anx | r ∈ R, ai ∈ R} is the group, under composition followed by truncation, of invertible, orientationpreserving real n-jets at 0. Consider the homomorphism D : Jn → R obtained by projecting o...