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Characteristic classes associated to complex vector bundles.
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characteristic classes of tangent bundle of 2-nd unordered configuration space
Given a (real or almost complex) manifold $M$, Let the 2-nd unordered configuration space be the quotient space
$$
B(M,2)=(M\times M\setminus\ \Delta)/\ \mathbb{Z}_2
$$
where
$$
\Delta=\{(m,m)\mid m\ …