Foundations of Combinatorial Topology
E681629
Foundations of Combinatorial Topology is a seminal mathematical monograph by Lev Pontryagin that systematically develops the methods and results of early 20th-century combinatorial (algebraic) topology.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Foundations of Combinatorial Topology canonical | 1 |
Statements (40)
| Predicate | Object |
|---|---|
| instanceOf |
mathematics book
ⓘ
monograph ⓘ topology book ⓘ |
| aim | to provide a rigorous foundation for combinatorial topology ⓘ |
| audience |
advanced graduate students in mathematics
ⓘ
research mathematicians ⓘ |
| author | Lev Pontryagin NERFINISHED ⓘ |
| contribution |
early systematic exposition of algebraic-topological methods
ⓘ
formalization of combinatorial approaches to topological spaces ⓘ |
| describes |
combinatorial methods in topology
ⓘ
homological invariants of complexes ⓘ |
| field |
algebraic topology
ⓘ
combinatorial topology ⓘ topology ⓘ |
| genre | mathematical monograph ⓘ |
| hasAuthorNationality |
Russian
ⓘ
Soviet ⓘ |
| historicalPeriod | early 20th-century topology ⓘ |
| influenced |
development of Soviet school of topology
ⓘ
later textbooks in algebraic topology ⓘ |
| influencedBy |
Henri Poincaré
NERFINISHED
ⓘ
L. E. J. Brouwer NERFINISHED ⓘ |
| mathematicalSubjectClassification |
55-XX Algebraic topology
ⓘ
57-XX Manifolds and cell complexes ⓘ |
| notableFor |
influence on algebraic topology
ⓘ
systematic development of early combinatorial topology ⓘ |
| originalLanguage | Russian ⓘ |
| publicationCentury | 20th century ⓘ |
| relatedConcept |
cellular decomposition
ⓘ
simplicial homology ⓘ topological invariance of Betti numbers ⓘ |
| relatedWork | Foundations of Algebraic Topology NERFINISHED ⓘ |
| topic |
Betti numbers
ⓘ
Euler characteristic NERFINISHED ⓘ cell complexes ⓘ continuous mappings ⓘ fundamental group ⓘ homology theory ⓘ simplicial complexes ⓘ topological invariants ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.