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• Tags
  • #homotopy/bundles
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Euler class

• The Euler class of the tangent bundle of an oriented manifold can be identified with the Euler characteristic times the fundamental class

• Fact: \(\widehat{{\mathbf{T}}}S^2 \underset{\operatorname{Diff}}{\cong} {\mathbf{RP}}^3\) are diffeomorphic, where the LHS is the unit tangent bundle.

Relation to BunG:

Relation to the Gysin sequence:

Formulas