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

{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...

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...

Chern's work, most notably the Chern-Gauss-Bonnet Theorem, Chern–Simons theory, and Chern classes, are still highly influential in current research in mathematics...

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

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

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_{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 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...

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...

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

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...

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

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...

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

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

_{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...

{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...

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...

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...

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

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...

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...

\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...

first Chern class; hence, it belongs to the completion of the equivariant cohomology ring.) In the non-equivariant case, the first Chern class can be...

topology of a U ( 1 ) {\displaystyle U(1)} bundle is classified by its Chern class, which is an element of H 2 ( M , Z ) {\displaystyle H^{2}(M,\mathbb...

In mathematics, ∞-Chern–Weil theory is a generalized formulation of Chern–Weil theory from differential geometry using the formalism of higher category...