In geometric topology, the de Rham invariant is a mod 2 invariant of a (4k+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 4k-dimensional invariant (either symmetric or quadratic, ), and the Kervaire invariant, a (4k+2)-dimensional quadratic invariant
It is named for Swiss mathematician Georges de Rham, and used in surgery theory.[1][2]
^Morgan, John W; Sullivan, Dennis P. (1974), "The transversality characteristic class and linking cycles in surgery theory", Annals of Mathematics, 2, 99 (3): 463–544, doi:10.2307/1971060, JSTOR 1971060, MR 0350748
^John W. Morgan, A product formula for surgery obstructions, 1978
In geometric topology, the deRhaminvariant is a mod 2 invariant of a (4k+1)-dimensional manifold, that is, an element of Z / 2 {\displaystyle \mathbf...
Georges deRham (French: [dəʁam]; 10 September 1903 – 9 October 1990) was a Swiss mathematician, known for his contributions to differential topology...
equestrian DeRham Farm in Philipstown, New York DeRham, Iselin & Moore DeRham curve DeRham cohomology DeRhaminvariantDeRham–Weil theorem Hodge–deRham spectral...
existence of "holes" in the manifold, and the deRham cohomology groups comprise a set of topological invariants of smooth manifolds that precisely quantify...
L^{4k}\cong L_{4k}} ), and the DeRhaminvariant, a ( 4 k + 1 ) {\displaystyle (4k+1)} -dimensional symmetric invariant L 4 k + 1 {\displaystyle L^{4k+1}}...
be used as the differential (coboundary) to define deRham cohomology on a manifold. The k-th deRham cohomology (group) is the vector space of closed k-forms...
Riemannian geometry in a more general setting. In 1952 Georges deRham proved the deRham decomposition theorem, a principle for splitting a Riemannian...
dimensions by Wolfgang Franz (1935) and Georges deRham (1936). Analytic torsion (or Ray–Singer torsion) is an invariant of Riemannian manifolds defined by Daniel...
in the 1980s. These invariants have many interesting relationships with several older branches of mathematics, including deRham theory, Hochschild (co)homology...
(Reidemeister torsion, R-torsion, Franz torsion, deRham torsion, Ray-Singer torsion), a topological invariant of manifolds Whitehead torsion, in geometric...
different types of cohomology was Georges deRham. One can use the differential structure of smooth manifolds via deRham cohomology, or Čech or sheaf cohomology...
groups and homogeneous spaces by relating cohomological methods of Georges deRham to properties of the Lie algebra. It was later extended by Claude Chevalley...
notion of a Weyl connection is conformally invariant, and the change in one-form is mediated by a deRham cocycle. An example of a Weyl connection is...
\Omega ^{3}(M)\to \cdots } The cohomology of this complex is called the deRham cohomology of M. Locally constant functions are designated with its isomorphism...
manifolds include the construction of smooth topological invariants of such manifolds, such as deRham cohomology or the intersection form, as well as smoothable...
{\displaystyle \Omega _{G}^{\bullet }(X)} which is the totalization of the de-Rham double complex of the groupoid. The terms in the Cartan complex are Ω G...
orientable. Additionally, if M is a closed symplectic manifold, then the 2nd deRham cohomology group H2(M) is nontrivial; this implies, for example, that the...
the proof of the Poincaré lemma, it can be shown that deRham cohomology is homotopy-invariant. In electrodynamics, the case of the magnetic field B →...
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