In mathematics, the Kervaire semi-characteristic, introduced by Michel Kervaire (1956), is an invariant of closed manifolds M of dimension
taking values in
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
is the de Rham invariant of