In mathematics, the Kervaire semi-characteristic, introduced by Kervaire (1956), is an invariant of manifolds M of dimension 4n+1 taking values in Z/2Z, given by
k(M) =Atiyah & Singer (1971) showed that it is given by the index of a skew-adjoint elliptic operator.
References
Kervaire semi-characteristic Wikipedia(Text) CC BY-SA