Abstract

Introduced the homological algebra and presented some interesting basic properties of the notion.In this paper we extend the above notion to homology groups and tried to proof the some similar basic properties of the topological homolog groups. We also studied more about the random graph groups of the homology order to find necessary and sufficient conditions for which the hematology is discrete. We followed the analytical induction mathematical method and we found that studying homology groups may be more important than cohomology groups.

Highlights

  • Algebra homology is twentieth century field of mathematics that can trace its origins and connection and homology is one of the main idea of algebraic topology

  • Rahman Abdel Gadir We followed the analytical induction mathematical method and we found that studying homology

  • Im (d) is antomatically closed, and there is no difference between L2- cohamology and ordinary cohomology with complex coefficients of Xin particular

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Summary

INTRODUCTION

Algebra homology is twentieth century field of mathematics that can trace its origins and connection and homology is one of the main idea of algebraic topology. Algebra's topology is one of the most important creation in mathematics which uses algebra tools to study homological groups.The most important of this invariants are homology groups, cohomology groups. The goal of this paper is to acquire uses study of some classes of algebraic homology (some underline geometry notation). Graph and topology theory and cohomological diminution of random graph groups

SIMPLICIAL COMPLEXES AND HOMOLOGY GROUPS
HOMOLOGICAL ALGEBRA
L2- COHAMOLOGY
COHOMOLOGY
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