Chern class

Chern class

Top Chern class is the Euler class.

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Properties

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Description in terms of \({\mathbf{B}}{\operatorname{U}}_n\)

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Stability

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Splitting principle

attachments/Pasted%20image%2020220403211858.png See flag variety.

Formulas

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Examples

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#examples/explicit-computations

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Exercises

#examples/exercises

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Links to this page

intersection theory

Warning: does not work in nonarchimedean geometry or complex analytic geometry. Problems: not enough cycles for a moving lemma, and not enough Chern classes
examples of fibrations

Used in analyzing Chern classes.
equivariant K theory

The natural home for equivariant Chern classes and Chern characters.
elliptic genera

- Tags: - #todo/untagged - Refs: - #todo/add-references - Links: - Jacobi theta - cobordism - Chern classes
Riemann-Roch

See Chern class.
Calabi-Yau

A compact Kahler manifold with vanishing first Chern class \(c_1 = 0\) which is Ricci-flat.
900_Changelog

2022-09-13 at 16h25 · Chern class
2021-10-05 quick_notes

Thom-Dold, Poincare duality, Chern classes

#homotopy/bundles #todo/add-references #examples/explicit-computations #examples/exercises