topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles. They have since...

In mathematics, the Chern–Weil homomorphism is a basic construction in Chern–Weil theory that computes topological invariants of vector bundles and principal...

{Pic} (X)\to \operatorname {Cl} (X),} known as the first Chern class. The first Chern class is injective if X is normal, and it is an isomorphism if X...

portal Chern classes Chern–Gauss–Bonnet theorem Chern–Simons theory Chern–Simons form Chern–Weil theory Chern–Weil homomorphism Chern-Lashof theory Chern-Bott...

bundle can be defined by means of the theory of Chern classes, and is encountered where Chern classes exist — most notably in differential topology, the...

fundamental characteristic classes known at that time (the Stiefel–Whitney class, the Chern class, and the Pontryagin classes) were reflections of the classical...

c_{2k}(E\otimes \mathbb {C} )} denotes the 2 k {\displaystyle 2k} -th Chern class of the complexification E ⊗ C = E ⊕ i E {\displaystyle E\otimes \mathbb...

conjectured that compact complex manifolds of Kähler type with vanishing first Chern class always admit Ricci-flat Kähler metrics, and Shing-Tung Yau (1978), who...

+c_{i-1}(A)c_{1}(C)+c_{i}(C).} It follows that the Chern classes of a vector bundle E {\displaystyle E} depend only on the class of E {\displaystyle E} in the Grothendieck...

after mathematicians Shiing-Shen Chern and James Harris Simons, who introduced the Chern–Simons 3-form. In the Chern–Simons theory, the action is proportional...

H^{2}(V,{\mathcal {O}}_{V})\to \cdots .} The first arrow is the first Chern class on the Picard group c 1 : P i c ( V ) → H 2 ( V , Z ) , {\displaystyle...

Thom isomorphism Generalized Gauss–Bonnet theorem Chern class Pontryagin class Stiefel-Whitney class Bott, Raoul and Tu, Loring W. (1982). Differential...

smooth structures (and thus the same first Chern class) but different holomorphic structures. The Chern class statements are easily proven using the exponential...

In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that...

_{t=0}^{i}{j+t-i-1 \choose t}w_{i-t}w_{j+t}.} Characteristic class for a general survey, in particular Chern class, the direct analogue for complex vector bundles...

Chern class, and thus provides equivalent information; the advantage of the Segre class is that it generalizes to more general cones, while the Chern...

{\displaystyle \mathbb {G} (1,3)} . In order to get the Euler class, the total Chern class of T ∗ {\displaystyle T^{*}} must be computed, which is given...

{E}}'\to {\mathcal {E}}\to {\mathcal {E}}''\to 0,} we can compute the total Chern class of E {\displaystyle {\mathcal {E}}} with the formula c ( E ) = c ( E...

\mathbb {Z} )} is the first Chern class map, sending an isomorphism class of a line bundle to its associated first Chern class. It turns out that there is...

complex vector bundle is a Chern class. A complex vector bundle is canonically oriented; in particular, one can take its Euler class. A complex vector bundle...

Chern may refer to: Shiing-Shen Chern (1911–2004), Chinese-American mathematician Chern class, a type of characteristics class associated to complex vector...

Hodge classes than the Chern classes of vector bundles and that the Chern classes of coherent sheaves are insufficient to generate all the Hodge classes. Consequently...

up to isomorphism by their Chern classes, which are integers: they lie in H2(CPn,Z) = Z. In fact, the first Chern classes of complex projective space...

is positive (since ω is then a Kähler form that represents the first Chern class of L in H2(X, Z)). The Kähler form ω that satisfies these conditions...

In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons...

manifold X {\displaystyle X} the second Stiefel-Whitney class can be computed as the first chern class mod  2 {\displaystyle {\text{mod }}2} . A genus g Riemann...

answer h times the second Chern class of the gauge bundle over M × S 1 {\displaystyle M\times S^{1}} . This second Chern class may be any integer. In particular...

three cases dependent on the sign of the first Chern class of the Kähler manifold: When the first Chern class is negative, there is always a Kähler–Einstein...

generator of negative degree. Hopf bundle Stiefel-Whitney class Euler sequence Chern class (Chern classes of tautological bundles is the algebraically independent...

According to Chern–Weil theory, the Ricci form of any such metric is a closed differential 2-form which represents the first Chern class. Calabi conjectured...