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Second Order Operators with Non-Zero Eta Invariant

Abstract We give an example of an elliptic second order pseudodifferential operator with a non-zero eta invariant. The operator is constructed on homogeneous bundles over compact Lie groups and is formed by composing differential operators and an operator of class In general it is not elliptic but in the special case of even dimensional bundles over SU(2) it is elliptic. The eta invariant is calculated in the special case and in the non elliptic case a difference eta invariant is obtained.