Research any topic before you write.

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

Supermanifold

In mathematics and mathematical physics, supermanifolds are generalizations of manifolds in which the algebra of functions includes both commuting and anticommuting variables. In the standard mathematical formulation, a smooth supermanifold is a locally ringed space whose structure sheaf is locally isomorphic to the tensor product of the ring of ordinary…

Standards & Products

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 Supermanifold. 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

Properties

Tangent sheaf

Super Riemann surfaces

Projective spaces

Examples

Batchelor's theorem

Odd symplectic structures

SUSY

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

Supermanifold

Nodes73
Edges72
Triples106
Avg. degree1.97
Density0.027397
Components1

How this topic connects Entity context

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

Supermanifold

Top relations

related to References · 26
Supermanifold → Albert, Bartocci, Batalin-Vilkovisky, BF02097392, Bibcode, Bruzzo, Classical, Communications, Connections, Dennis Gaitsgory, Fall TermSchwarz, Geometry, Hernandez Ruiperez, IAS, ISBN, Joseph Bernstein, Kluwer, Lectures, Mangiarotti, Mathematical Physics
related to Odd symplectic form · 12
Supermanifold → All, An, Darboux, Grassmann-even, Grassmann-odd, In, Its, P-manifold, P-manifolds, Such, There, TM
related to Concrete: as a smooth manifold · 8
Supermanifold → DeWitt, Grassmann, In, Its, Lambda, One, Rogers, To
related to SUSY · 8
Supermanifold → Frobenius, GL, If, SUSY-manifold, SUSY-structure, TM, TM/P, With
related to P and SP-manifolds · 7
Supermanifold → Darboux, Equivalently, P-manifolds, P-transformations, SP-manifold, SP-transformations, Using
related to Super Riemann surfaces · 7
Supermanifold → CP, Equivalently, In, Lie, Riemann, TM, TM/D
related to Examples · 6
Supermanifold → In, Let, Lie, More, The, Then
related to Tangent sheaf · 6
Supermanifold → An, Der, Its, The, This, Thus
related to Properties · 5
Supermanifold → An, In, Instead, OM, Unlike
related to Antibracket · 4
Supermanifold → Equipped, Given, Here, Poisson

Important terminology Word statistics

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

Important terminology

displaystyle odd space mathbb functions locally structure sheaf manifold smooth one theta supermanifolds even called mathematical definition symplectic form ringed

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Supermanifoldis alocally ringed space whose structure sheaf is locally isomorphic to the tensor product of the ring of ordinary smooth functions C0.90text
Supermanifoldis aspace equipped with a sheaf of supercommutative algebras that is locally isomorphic to a superdomain.A more concrete coordinate-based formalism0.90text
Supermanifoldis aclosed0.90text
quantum field theoryinstance ofThey were introduced in connection with supersymmetry and are used in areas of mathematical physics0.80text
string theoryinstance ofThey were introduced in connection with supersymmetry and are used in areas of mathematical physics0.80text
as well as in purely mathematical subjects including the theory of Lie superalgebrasinstance ofThey were introduced in connection with supersymmetry and are used in areas of mathematical physics0.80text
supergroupsinstance ofThey were introduced in connection with supersymmetry and are used in areas of mathematical physics0.80text
Supermanifoldrelated to Algebro-geometric: as a locally ringed spaceThe0.60section
Supermanifoldrelated to Algebro-geometric: as a locally ringed spaceMore0.60section
Supermanifoldrelated to Algebro-geometric: as a locally ringed spaceLambda0.60section
Supermanifoldrelated to AntibracketGiven0.60section
Supermanifoldrelated to AntibracketPoisson0.60section

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.