De Rham invariant

In geometric topology, the de Rham invariant is a mod 2 invariant of a (4k+1)-dimensional manifold, that is, an element of ${\displaystyle \mathbf {Z} /2}$ – either 0 or 1. It can be thought of as the simply-connected symmetric L-group ${\displaystyle L^{4k+1},}$ and thus analogous to the other invariants from L-theory: the signature, a 4k-dimensional invariant (either symmetric or quadratic, ${\displaystyle L^{4k}\cong L_{4k}}$), and the Kervaire invariant, a (4k+2)-dimensional quadratic invariant ${\displaystyle L_{4k+2}.}$

...
Wikipedia