theory, Chern–Simons theory, knot theory, Gromov–Witten invariants. Chern classes were introduced by Shiing-Shen Chern (1946). Chern classes are characteristic...

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...

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

In algebraic geometry, a localized Chern class is a variant of a Chern class, that is defined for a chain complex of vector bundles as opposed to a single...

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...

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

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

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

{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...

originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions...

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...

+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...

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...

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...

{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...

{\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...

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

stack Approximation property – Mathematical concept Barsotti–Tate group Chern class Crystal (mathematics) – Cartesian sections of certain fibered categoriesPages...

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

connection), then the underlying principal bundle must have trivial Chern classes, which is a topological obstruction to the existence of flat connections:...

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...

\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 there is an...

_{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...

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...

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...

first Chern class. A proposal of Calabi's suggested that Kähler–Einstein metrics exist on any compact Kähler manifolds with positive first Chern class which...

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

Chow groups. The arithmetic Riemann–Roch theorem then describes how the Chern class behaves under pushforward of vector bundles under a proper map of arithmetic...