Lefschetz fixed-point theorem
GPTKB entity
Statements (20)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
compact topological spaces
continuous maps |
| gptkbp:category |
gptkb:topology
fixed-point theorems |
| gptkbp:field |
gptkb:topology
|
| gptkbp:generalizes |
gptkb:Brouwer_fixed-point_theorem
|
| gptkbp:hasConcept |
gptkb:Lefschetz_number
homology trace of induced map on homology |
| https://www.w3.org/2000/01/rdf-schema#label |
Lefschetz fixed-point theorem
|
| gptkbp:influenced |
gptkb:Atiyah–Bott_fixed-point_theorem
gptkb:Lefschetz_hyperplane_theorem |
| gptkbp:introducedIn |
1926
|
| gptkbp:namedAfter |
gptkb:Solomon_Lefschetz
|
| gptkbp:state |
If the Lefschetz number of a continuous map from a compact oriented manifold to itself is nonzero, then the map has a fixed point.
|
| gptkbp:bfsParent |
gptkb:Solomon_Lefschetz
gptkb:Atiyah–Bott_fixed-point_theorem gptkb:Algebraic_number_theory |
| gptkbp:bfsLayer |
5
|