Mathematics Branches, Topics, and Sub-Topics

A structured visual guide to the major mathematical areas and their relationships.

Search by code, branch, topic, subtopic, or a keyword from the descriptions.

20Jxx Connections with homological algebra

This subtopic studies connections with homological algebra, where group-theoretic questions are analyzed using homology, cohomology, and derived constructions.

Specific topics

20J05 Homological methods in group theory

Overview

20J05 studies homological methods in group theory in connections with homological algebra. It uses homological tools to analyze group extensions, cohomology, and categorical constructions associated with groups.

Related Wikipedia Page

Connections With Homological Algebra (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for homological methods in group theory
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to compute group cohomology, compare extensions, and apply derived methods.

Applications

  • Group cohomology
  • Derived and categorical methods
  • Extensions and homological invariants

References

Recommended Textbooks

20J06 Cohomology of groups

Overview

20J06 studies cohomology of groups in connections with homological algebra. It uses homological tools to analyze group extensions, cohomology, and categorical constructions associated with groups.

Related Wikipedia Page

Connections With Homological Algebra (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for cohomology of groups
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to compute group cohomology, compare extensions, and apply derived methods.

Applications

  • Group cohomology
  • Derived and categorical methods
  • Extensions and homological invariants

References

Recommended Textbooks

20J15 Category of groups

Overview

20J15 studies category of groups in connections with homological algebra. It uses homological tools to analyze group extensions, cohomology, and categorical constructions associated with groups.

Related Wikipedia Page

Connections With Homological Algebra (Wikipedia)

Useful Links

Key Ideas

  • Canonical formulations and representative examples for category of groups
  • How structural, local, and computational viewpoints interact in the subject
  • Standard theorem patterns and invariants used in current research practice

Typical Uses

Used to compute group cohomology, compare extensions, and apply derived methods.

Applications

  • Group cohomology
  • Derived and categorical methods
  • Extensions and homological invariants

References

Recommended Textbooks