Segal conjecture
E886937
The Segal conjecture is a fundamental result in algebraic topology that relates the Burnside ring of a finite group to the stable cohomotopy of its classifying space, profoundly influencing equivariant stable homotopy theory.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Segal conjecture canonical | 1 |
Statements (25)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical conjecture
ⓘ
theorem in algebraic topology ⓘ |
| appliesTo | finite group G ⓘ |
| concerns |
Burnside ring
ⓘ
classifying space of a finite group ⓘ finite groups ⓘ stable cohomotopy ⓘ |
| describes | relationship between A(G) and stable cohomotopy of BG ⓘ |
| field |
algebraic topology
ⓘ
equivariant stable homotopy theory ⓘ |
| hasConsequence | identification of stable cohomotopy of BG with completion of A(G) ⓘ |
| hasDomain | equivariant homotopy theory ⓘ |
| hasImpactOn |
fixed point theory in topology
ⓘ
representation theory of finite groups ⓘ |
| implies | completion theorem for the Burnside ring ⓘ |
| influenced | development of equivariant stable homotopy theory ⓘ |
| isConsidered | fundamental result in algebraic topology ⓘ |
| namedAfter | Graeme Segal NERFINISHED ⓘ |
| originallyFormulatedBy | Graeme Segal NERFINISHED ⓘ |
| relates |
Burnside ring of a finite group
NERFINISHED
ⓘ
stable cohomotopy of the classifying space of a finite group ⓘ |
| status | proved ⓘ |
| usesConcept |
Burnside ring A(G)
NERFINISHED
ⓘ
classifying space BG ⓘ stable homotopy category ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.