Thom Isomorphism

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External reading guide · Graduate

A Thom class shifts cohomology from a vector bundle's base into the relative cohomology of its disk and sphere bundles. Track the orientation hypothesis when moving from mod-two to integer coefficients.

Before opening the references

Smooth Vector Bundle · singular cohomology · cup product · orientation of a smooth manifold

Where to read

  1. Start here: Algebraic Topology

    Allen Hatcher · Book · English · Free full text

    §4.D Cohomology of Fiber Bundles, Corollary 4D.9 (Thom isomorphism) and Theorem 4D.10 (existence of Thom classes), printed pp. 441–442

    Source page · Checked 2026-10-16

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