Stiefel–Whitney Classes

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External reading guide · Graduate

These mod-two cohomology classes detect features of real vector bundles that survive pullback. Start with the axioms and Whitney sum formula, then relate the classes to obstructions to independent sections.

Before opening the references

Smooth Vector Bundle · singular cohomology · cup product

Where to read

  1. Start here: Vector Bundles & K-Theory (Version 2.2)

    Allen Hatcher · Book draft · English · Free full text

    §3.1 Stiefel-Whitney and Chern Classes, Axioms and Construction, Theorem 3.1 (naturality and Whitney sum formula); §3.3 Characteristic Classes as Obstructions

    Source page · Checked 2026-10-16

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