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