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Let $X$ be a complex manifold and $Y\subseteq X$ a submanifold. It is well known that the Thom class of the normal bundle of $Y$ over $X$ is the Poincaré dual to the homology class [Y]. I read that this result is important because we can give an explicit construction of the Thom class, specially when the bundle is trivial.

Is it true that the normal bundle in this case is always trivial? Where can I find the explicit constructions of the Thom class (at least for trivial bundles)? What extra information gives us the thom class about the Poincaré dual?

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I know you are looking at complex manifolds and complex geometry, but a great place to read about these things in the real setting is Bott and Tu's Differential forms in Algebraic Topology – M Turgeon Jul 27 '12 at 12:53

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