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In mathematics, the Kervaire semi-characteristic, introduced by Michel Kervaire (1956), is an invariant of closed manifolds M of dimension taking values in , given by
where F is a field.
Michael Atiyah and Isadore Singer (1971) showed that the Kervaire semi-characteristic of a differentiable manifold is given by the index of a skew-adjoint elliptic operator.
Assuming M is oriented, the Atiyah vanishing theorem states that if M has two linearly independent vector fields, then .[1]
The difference is the de Rham invariant of .[2]