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Simple homotopy theoryHomotopy theoryHurewicz theoremGroup cohomologyGraph homologyStability theoryRelative homologyEquivariant cohomologyHomological algebraFundamental groupMorphismK-stabilityStable manifoldGalois cohomologyTopological propertyCohomologyLefschetz fixed-point theoremGeneral topologyGeometric topologyHomotopy type theoryIsomorphism theoremsCategory of topological spacesClass field theoryCartan decompositionModel categoryBott periodicity theoremNatural transformationHomomorphismCohomology ringHomotopy groupAlgebraic analysisHom functorAffine groupMorse homologyHomotopy groups of spheresGeometric group theorySimplicial homologyInvariant theoryMathematical morphologyDerived categoryHodge structureIntersection theoryLog structureAlgebraic combinatoricsToposInvariant manifoldHomeomorphismClosed monoidal categoryMeasurable functionCovering groupPushforwardSubmanifoldLocal homeomorphismStructureRing theoryOperator algebraOperator theoryAlgebraic number theoryComparison of topologiesAlgebraic groupDifferential topologyInitial and terminal objectsSpectral theorySymmetry groupMapping class groupSubcategoryAlgebra homomorphismTopologyHodge theoryGeometric transformationProjective geometryHolomorphic vector bundleIsogenyAlgebraic topologySymplectic geometryModuli spaceClosed graph theoremResolvent formalismIsometry groupDynamical systems theoryDifferential graded algebraCombinatorial designEuclidean topologySpectral sequenceSemi-simplicitySymmetric groupRepresentation theoremTransformation geometryCompact-open topologyOutline of category theoryRing homomorphismSpectrumContact geometryGlobal analysisSheaf cohomologyCoherent sheafExcision theoremRepresentation theoryGraph homomorphismLimit