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Cartan decompositionProductProduct topologyEuclidean groupAssociated bundleModuli spaceSegre embeddingMapping class groupTensor product of representationsGroup actionLattice of subgroupsCayley graphAlgebraic torusEuclidean topologyFundamental groupSubmanifoldAdjunction formulaCategory theoryComplex lie groupIsometry groupToposOrthogonal groupLie algebra representationProjectivizationEuler classDistributionGraph of a functionArithmetic groupTensor fieldGeometryCoproductModular groupConformal geometryGauge theoryCoarea formulaSimplicial complexCoordinate systemGroup extensionPartially ordered setCharacter tableCompact groupCotangent bundleSelberg trace formulaPrime elementLatticeNoncommutative geometryGeometric group theoryDiagonal morphismGroup schemeRepresentationTangent spaceCartesian productTensor product of modulesSpace groupModuli of algebraic curvesLength functionGeometric topologyCharacteristic classHolomorphic vector bundleMinkowski spaceGalois groupSesquilinear formAlgebraic groupFundamental representationPseudo-euclidean spaceClass field theoryAbelian varietyHodge star operatorConnectorMetric tensorCohomologyGermBraid groupCoherent sheafLinear formAffine groupIsomorphism theoremsAdjoint representationCartesian tensorFunctional analysisCharacter theoryComparison of topologiesBundle mapMathematical structureChern classCanonical bundleCausal structureRepresentation of a lie groupPermutation groupGroup cohomologyBundleSpectral tripleProduct categoryGalois connectionFundamental group schemeCantor spaceTensor productDifferential invariantCanonical mapHopf fibration