On multilinear oscillatory integrals, nonsingular and singular

By Michael Christ, Xiaochun Li, Terence Tao, C. Thiele. 2003

66 citations recorded by the source corpus.

Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant differential forms. In this paper, we construct an explicit cochain map from the small Cartan model into the standard Cartan model, inducing an isomorphism in cohomology. The construction involves the solution of a remarkable inhomogeneous Maurer-Cartan equation. This solution has further applications to the theory of transgression in the Weil algebra, and to the Chevalley-Koszul theory of the cohomology of principal bundles.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f9ce7914c3ec87931b4d47aa7de33d9223161bb2

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. J. Stasheff
2. Xiaochun Li
3. H. Kajiura
4. H. Lenzing

In Geometry and Topology

1. J. Stasheff
2. Xiaochun Li
3. H. Kajiura
4. Jonathan Bennett
5. Michael T. Lacey
6. H. Lenzing

In Mathematical Physics

1. Xiaochun Li
2. Michael T. Lacey
3. J. Stasheff
4. H. Kajiura
5. Jonathan Bennett
6. Tuomas Hytönen
7. D. Cruz-Uribe
8. Larry Guth

Citations in the corpus

• Homotopy Algebras Inspired by Classical Open-Closed String Field Theory (2004, background): “Remark 6 The concept was later reintroduced by Flato, Gerstenhaber and Voronov [9] under the name Leibniz pair, cf. also [ 2 ].”
• Bilinear Hilbert transforms along curves, I: the monomial case (2008, methodology): “” Fourier analysis. BILINEAR HILBERT TRANSFORMS ALONG CURVES, I 19 7. Uniformity We introduce a concept related to a notion of uniformity employed by Gowers [10]. A similar uniformity was utilized in [4]. Let σ ∈ (0,1], let Q be a collection of some real-valued measurable functions, and fix a bounded”
• Aspects of Multilinear Harmonic Analysis Related to Transversality (2014, background): “The finiteness condition (46) is somewhat difficult to interpret in general, although under certain 11For closely related multilinear oscillatory integral inequalities, that may also be viewed as oscillatory Brascamp–Lieb inequalities, see [26], [25] and [12].”
• Carleson's Theorem: Proof, Complements, Variations (2003, background): “e integral above is bounded. The proof demonstrates a multilinear variant of the van der Corput type inequality, of which Lemma 9.13 is just one example. More generally, M. Christ, Li, Tao and Thiele [20] define multilinear functionals (9.24) Λλ(f1,f2,··· ,fn) = Z Rm eiλP(x) Yn j=1 fj(πj(x))η(x)dx wh”