 Euler class of an oriented odd-rank vector bundle is two-torsion

ID: euler-class-of-an-oriented-odd-rank-vector-bundle-is-two-torsion

E

of odd rank, multiplication by

- 1

on each fiber identifies

E

with the oppositely oriented bundle. Naturality and reversal of the Thom class give

e (E) = e (E^{op}) = - e (E),

2 e (E) = 0

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