Kervaire semi-characteristic

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) = $\sum_{i=0}^n \dim H^{2i}(M,R)\bmod 2$

Atiyah & Singer (1971) showed that it is given by the index of a skew-adjoint elliptic operator.

References

• Atiyah, Michael F.; Singer, Isadore M. (1971), "The Index of Elliptic Operators V", Annals of Mathematics. Second Series (The Annals of Mathematics, Vol. 93, No. 1) 93 (1): 139–149, doi:10.2307/1970757, JSTOR 1970757
• Kervaire, Michel (1956), "Courbure intégrale généralisée et homotopie", Mathematische Annalen 131: 219–252, doi:10.1007/BF01342961, ISSN 0025-5831, MR 0086302