KnowraAlgebraic topologyLinked fromLinked fromThe 18 pages that link to Algebraic topology, each with the reason it gives.All 18Broader topic 2Related 5Narrower topic 9Compared with 2Henri PoincaréRelated: Poincaré’s foundational work helped establish this field and introduced the fundamental group.TopologyBroader topic: It turns spaces into computable groups and invariants for comparison.Category theoryRelated: Functoriality explains how continuous maps induce maps on algebraic invariants.Homological algebraNarrower topic: Homological algebra grew partly from the need to formulate and calculate topological homology systematically.Geometric measure theoryCompared with: It tracks qualitative shape, whereas geometric measure theory also quantifies area and mass.CategoryNarrower topic: Category theory was first developed to organize constructions in algebraic topology.Samuel EilenbergBroader topic: It was a central field of Eilenberg’s research and teaching.Differential topologyCompared with: It often forgets smooth structure, while differential topology uses smooth maps and derivatives.Jean-Pierre SerreNarrower topic: Serre’s early work helped make spectral sequences and homotopy methods central to the field.Saunders Mac LaneRelated: Questions about natural constructions in topology helped motivate category theory’s creation.Henri CartanNarrower topic: Cartan’s cohomological methods became foundational tools in this field.Mikhail GromovNarrower topic: Several of Gromov’s geometric methods drew on and reshaped topological ideas.General topologyRelated: It converts topological questions into algebraic ones, complementing point-set methods.Poincaré dualityNarrower topic: The theorem is a landmark relation between algebraic invariants of spaces.Pavel AlexandrovRelated: Alexandrov helped organize and advance this field within Soviet mathematics.Seifert–Van Kampen theoremNarrower topic: The theorem exemplifies the use of algebra to extract global information from local pieces.Whitehead theoremNarrower topic: The theorem exemplifies how algebraic invariants can detect topological equivalence.Eilenberg–Zilber theoremNarrower topic: The theorem supplies a chain-level tool for computing topological invariants of products.
KnowraAlgebraic topologyLinked fromLinked fromThe 18 pages that link to Algebraic topology, each with the reason it gives.All 18Broader topic 2Related 5Narrower topic 9Compared with 2Henri PoincaréRelated: Poincaré’s foundational work helped establish this field and introduced the fundamental group.TopologyBroader topic: It turns spaces into computable groups and invariants for comparison.Category theoryRelated: Functoriality explains how continuous maps induce maps on algebraic invariants.Homological algebraNarrower topic: Homological algebra grew partly from the need to formulate and calculate topological homology systematically.Geometric measure theoryCompared with: It tracks qualitative shape, whereas geometric measure theory also quantifies area and mass.CategoryNarrower topic: Category theory was first developed to organize constructions in algebraic topology.Samuel EilenbergBroader topic: It was a central field of Eilenberg’s research and teaching.Differential topologyCompared with: It often forgets smooth structure, while differential topology uses smooth maps and derivatives.Jean-Pierre SerreNarrower topic: Serre’s early work helped make spectral sequences and homotopy methods central to the field.Saunders Mac LaneRelated: Questions about natural constructions in topology helped motivate category theory’s creation.Henri CartanNarrower topic: Cartan’s cohomological methods became foundational tools in this field.Mikhail GromovNarrower topic: Several of Gromov’s geometric methods drew on and reshaped topological ideas.General topologyRelated: It converts topological questions into algebraic ones, complementing point-set methods.Poincaré dualityNarrower topic: The theorem is a landmark relation between algebraic invariants of spaces.Pavel AlexandrovRelated: Alexandrov helped organize and advance this field within Soviet mathematics.Seifert–Van Kampen theoremNarrower topic: The theorem exemplifies the use of algebra to extract global information from local pieces.Whitehead theoremNarrower topic: The theorem exemplifies how algebraic invariants can detect topological equivalence.Eilenberg–Zilber theoremNarrower topic: The theorem supplies a chain-level tool for computing topological invariants of products.