De Rham invariant

In geometric topology, the de Rham invariant is a mod 2 invariant of a (4"k"+1)-dimensional manifold, that is, an element of formula_1 – either 0 or 1. It can be thought of as the simply-connected "symmetric" L-group formula_2 and thus analogous to the other invariants from L-theory: the signature, a 4"k"-dimensional invariant (either symmetric or quadratic, formula_3), and the Kervaire invariant, a (4"k"+2)-dimensional "quadratic" invariant formula_4
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: