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}^{2n}\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, JSTOR 1970757, doi:10.2307/1970757
Kervaire, Michel (1956), "Courbure intégrale généralisée et homotopie", Mathematische Annalen, 131: 219–252, ISSN 0025-5831, MR 0086302, doi:10.1007/BF01342961

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.