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Homotopy TheoryTriangulated CategoryCyclic HomologyNoncommutative GeometryIndex TheoremIndex TheoryModel CategoryAlgebraic CobordismHopf AlgebraSpectral SequencesResolution of SingularitiesSpectral FlowDirac OperatorsHochschild HomologyDirac OperatorAdams Spectral SequenceElementary SubgroupPerfect FieldHomotopy InvarianceAlgebraic Geometry