De Rham invariant
Introduction In geometric topology, the '''de Rham invariant''' is a mod 2 invariant of a (4''k''+1)-dimensional manifold, that is, an element of  – either 0 or 1.It can be thought of as the simply-connected ''symmetric'' L-group  and thus analogous to the other invariants from L-theory: the signature, a 4''k''-dimensional invariant (either symmetric or quadratic, ), and the Kervaire invariant, a (4''k''+2)-dimensional ''quadratic'' invariant It is named for Swiss mathematician Georges de Rham, and used in surgery theory.
Definition The de Rham invariant of a (4''k''+1)-dimensional manifold can be defined in various equivalent ways:* the rank of the 2-torsion in  as an integer mod 2;* the Stiefel–Whitney number ;* the (squared) Wu number,  where  is the Wu class of the normal bundle of  and  is the Steenrod square; formally, as with all characteristic numbers, this is evaluated on the fundamental class: ;* in terms of a semicharacteristic.
References * * Chess, Daniel, '' A Poincaré-Hopf type theorem for the de Rham invariant,'' 1980