theory, Chern–Simons theory, knot theory, Gromov–Witten invariants. Chern classes were introduced by Shiing-Shen Chern (1946). Chern classes are characteristic...
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portal Chern classes Chern–Gauss–Bonnet theorem Chern–Simons theory Chern–Simons form Chern–Weil theory Chern–Weil homomorphism Chern-Lashof theory Chern-Bott...
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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...
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In mathematics, the Chern–Weil homomorphism is a basic construction in Chern–Weil theory that computes topological invariants of vector bundles and principal...
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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...
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fundamental characteristic classes known at that time (the Stiefel–Whitney class, the Chern class, and the Pontryagin classes) were reflections of the classical...
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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...
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In mathematics, the Chern theorem (or the Chern–Gauss–Bonnet theorem after Shiing-Shen Chern, Carl Friedrich Gauss, and Pierre Ossian Bonnet) states that...
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Chern class, and thus provides equivalent information; the advantage of the Segre class is that it generalizes to more general cones, while the Chern...
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Chern may refer to: Shiing-Shen Chern (1911–2004), Chinese-American mathematician Chern class, a type of characteristics class associated to complex vector...
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originally defined as compact Kähler manifolds with a vanishing first Chern class and a Ricci-flat metric, though many other similar but inequivalent definitions...
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Divisor (algebraic geometry) (redirect from Divisor class)
{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...
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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...
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+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...
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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...
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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...
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Euler sequence (section Chern classes)
{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...
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Schubert calculus (redirect from Schubert class)
{\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...
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smooth structures (and thus the same first Chern class) but different holomorphic structures. The Chern class statements are easily proven using the exponential...
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stack Approximation property – Mathematical concept Barsotti–Tate group Chern class Crystal (mathematics) – Cartesian sections of certain fibered categoriesPages...
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Thom isomorphism Generalized Gauss–Bonnet theorem Chern class Pontryagin class Stiefel-Whitney class Bott, Raoul and Tu, Loring W. (1982). Differential...
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_{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...
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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...
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Yang–Mills equations (section Chern–Simons theory)
connection), then the underlying principal bundle must have trivial Chern classes, which is a topological obstruction to the existence of flat connections:...
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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...
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\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...
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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...
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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...
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In mathematics, the Chern–Simons forms are certain secondary characteristic classes. The theory is named for Shiing-Shen Chern and James Harris Simons...
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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...
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