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searching for ∞-Chern–Weil theory 25 found (28 total)

Foundations of Differential Geometry (675 words) [view diff] no match in snippet view article find links to article

curvature representation of characteristic classes of principal bundles (Chern–Weil theory), it covers Euler classes, Chern classes, and Pontryagin classes.

Calabi conjecture (1,563 words) [view diff] no match in snippet view article find links to article

setting of Kähler metrics on closed complex manifolds. According to Chern–Weil theory, the Ricci form of any such metric is a closed differential 2-form

Chern class (7,509 words) [view diff] no match in snippet view article find links to article

was in fact equivalent to his. The resulting theory is known as the Chern–Weil theory. There is also an approach of Alexander Grothendieck showing that

List of things named after André Weil (118 words) [view diff] no match in snippet view article find links to article

Bergman–Weil formula Borel–Weil theorem Chern–Weil homomorphism Chern–Weil theory De Rham–Weil theorem Weil's explicit formula Hasse-Weil bound Hasse–Weil

Hitchin–Thorpe inequality (919 words) [view diff] no match in snippet view article find links to article

and defines a continuous real-valued function on M. According to Chern-Weil theory, if M is oriented then the Euler characteristic and signature of M

Circle bundle (993 words) [view diff] no match in snippet view article find links to article

{\displaystyle U(1)} -bundle. Moreover, the characteristic classes from Chern-Weil theory of the U ( 1 ) {\displaystyle U(1)} -bundle agree with the characteristic

Seiberg–Witten flow (1,192 words) [view diff] no match in snippet view article find links to article

{\displaystyle F_{A}=\mathrm {d} A} , it can also be calculated using Chern–Weil theory: − 8 π 2 c 1 ( L ) = ∫ B tr ⁡ ( F A ∧ F A ) d vol g = ∫ B | F A +

Kervaire semi-characteristic (279 words) [view diff] no match in snippet view article find links to article

1016/0040-9383(73)90006-2. MR 0362367. Zhang, Weiping (2001-09-21). Lectures on Chern–Weil theory and Witten deformations. Nankai Tracts in Mathematics. Vol. 4. River

Shiing-Shen Chern (6,184 words) [view diff] no match in snippet view article find links to article

Topological phases of matter and Topological quantum field theory. Chern–Weil theory linking curvature invariants to characteristic classes from 1944 class

Chern–Simons theory (3,591 words) [view diff] no match in snippet view article find links to article

curvature properties of smooth manifolds M as de Rham cohomology (Chern–Weil theory), which is an important step in the theory of characteristic classes

Characteristic class (1,472 words) [view diff] no match in snippet view article find links to article

class Informally, characteristic classes "live" in cohomology. By Chern–Weil theory, these are polynomials in the curvature; by Hodge theory, one can

Classifying space (1,893 words) [view diff] no match in snippet view article find links to article

spaces may be complicated. In relation with differential geometry (Chern–Weil theory) and the theory of Grassmannians, a much more hands-on approach to

Ricci-flat manifold (1,883 words) [view diff] no match in snippet view article find links to article

be zero. The necessity of this condition was previously known by Chern–Weil theory. Beyond Kähler geometry, the situation is not as well understood.

Pontryagin class (1,906 words) [view diff] no match in snippet view article find links to article

depend polynomially on the curvature form of a vector bundle. This Chern–Weil theory revealed a major connection between algebraic topology and global

Chern's conjecture (affine geometry) (1,519 words) [view diff] no match in snippet view article

T M {\displaystyle TM} admit a compatible metric, and therefore, Chern–Weil theory cannot be used in general to write down the Euler class in terms of

Hermitian Yang–Mills connection (1,048 words) [view diff] no match in snippet view article find links to article

compact, λ ( E ) {\displaystyle \lambda (E)} may be computed using Chern–Weil theory. Namely, we have deg ⁡ ( E ) := ∫ X c 1 ( E ) ∧ ω n − 1 = i 2 π ∫

André Weil (3,111 words) [view diff] no match in snippet view article find links to article

List Bergman–Weil formula Borel–Weil theorem Chern–Weil homomorphism Chern–Weil theory De Rham–Weil theorem Weil's explicit formula Hasse–Weil Bound Hasse–Weil

Equivariant cohomology (1,813 words) [view diff] no match in snippet view article find links to article

{\displaystyle H^{*}(EG\times _{G}M)=H_{G}^{*}(M)} . (In order to apply Chern–Weil theory, one uses a finite-dimensional approximation of EG.) Alternatively

Connection (principal bundle) (3,441 words) [view diff] no match in snippet view article

connection over X. Dupont, Johan (August 2003). "Fibre Bundles and Chern-Weil Theory" (PDF). Archived from the original (PDF) on 31 March 2022. Eguchi

Chiral anomaly (3,296 words) [view diff] no match in snippet view article find links to article

F_{A}\rangle :=\operatorname {tr} \left(F_{A}\wedge F_{A}\right)} . Chern–Weil theory shows that this 4-form is locally but not globally exact, with potential

Séminaire Nicolas Bourbaki (1950–1959) (2,319 words) [view diff] no match in snippet view article

Koszul, Cohomologie des espaces fibrés différentiables et connexions (Chern–Weil theory) Jean Delsarte, Nombre de solutions des équations polynomiales sur

Yang–Mills equations (3,770 words) [view diff] no match in snippet view article find links to article

{\displaystyle F_{A}=dA+{\frac {1}{2}}[A,A]} vanishes. However, by Chern–Weil theory if the curvature F A {\displaystyle F_{A}} vanishes (that is to say

Colloquium Lectures (AMS) (2,186 words) [view diff] no match in snippet view article

topology: New and old directions; 2) The Kervaire invariant problem; 3) Chern-Weil theory and abstract homotopy theory. 2016 Timothy A. Gowers (University of

List of Chinese Americans (9,074 words) [view diff] no match in snippet view article find links to article

differential geometry and topology; known for Chern-Simons theory, Chern-Weil theory, Chern classes Chia-Kun Chu (朱家琨) – applied mathematician, Fu Foundation

Shing-Tung Yau (10,540 words) [view diff] no match in snippet view article find links to article

converge to a subsheaf which can be verified to be destabilizing by Chern–Weil theory. Like the Calabi–Yau theorem, the Donaldson–Uhlenbeck–Yau theorem