Research any topic before you write.

Find related topics. | Discover entities. | See connections. | Build a topical map.

Local system

In mathematics, a local system (or a system of local coefficients) on a topological space X is a tool from algebraic topology which interpolates between cohomology with coefficients in a fixed abelian group A, and general sheaf cohomology in which coefficients vary from point to point. Local coefficient systems were introduced by Norman Steenrod in 1943.

Applications, Examples & Overview

Use the mouse wheel or two fingers (on touchscreens) to zoom in and out of the map.

Research this topic

Explore the main themes, entities and connections around Local system. Start with the topic map, then use the sections below for research and deeper semantic analysis.

Explore this topic

Start with a few of the strongest sections from the source topic. These are research directions, not a list of keywords you must use.

Topics to explore

Browse the full topic structure. Each item opens a new analysis centered on that subject.

Overview

Definition

Examples

Cohomology

Applications

Advanced semantic analysis

Deeper signals for content research, entity SEO and topical coverage. The plain-language headings explain what each technical view is useful for.

Map overview Semantic statistics

Local system

Nodes40
Edges39
Triples30
Avg. degree1.95
Density0.05
Components1

How this topic connects Entity context

See the strongest relationship patterns around the current topic before diving into the raw triples.

Local system

Top relations

related to External links · 21
Local system → An, Christian, Computing Cohomology, December, Discusses, El Zein, Fouad, Geordie, Intersection, Jawad, Local, Local Systems, MacPherson, PDF, Rham, Robert, Schnell, Snoussi, Stack Exchange, What
related to Generalization · 3
Local system → For, Local, These
related to Cohomology · 2
Local system → Given, There
related to Definition · 2
Local system → In, Let
is a · 1
Local system → covariant functor L

Important terminology Word statistics

Use these terms to understand the vocabulary surrounding the topic, not as a checklist for keyword stuffing.

Important terminology

displaystyle local system cohomology systems mathcal sheaf pi mathbb constant groups given abelian sheaves text sections group locally widetilde connection

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Local systemis acovariant functor L0.90text
Qinstance ofExamples Constant sheaves0.80text
Local systemrelated to CohomologyThere0.60section
Local systemrelated to CohomologyGiven0.60section
Local systemrelated to DefinitionLet0.60section
Local systemrelated to DefinitionIn0.60section
Local systemrelated to External linksWhat0.60section
Local systemrelated to External linksStack Exchange0.60section
Local systemrelated to External linksSchnell0.60section
Local systemrelated to External linksChristian0.60section
Local systemrelated to External linksComputing Cohomology0.60section
Local systemrelated to External linksLocal Systems0.60section

Related concept clusters Concept neighborhoods

These clusters group vocabulary that occurs around closely connected concepts in the source material.

    Connections between topic areas Semantic bridges

    Bridges can reveal useful research angles that are easy to miss in a flat list of related terms.

    Min side: 3
    For writers, content strategists, SEOs, marketers and creators — from quick topic research to advanced semantic analysis.