= Cohomology class of a cooriented submanifold
{title2=$\varepsilon_Y\in H^{\operatorname{codim}Y}(X;\mathbb Z)$}
An oriented normal bundle of a compact embedded <submanifold> has a <Thom class>. A <tubular neighborhood> and excision identify it with a relative class in $H^d(X,X\setminus Y)$. Its image in absolute <cohomology> is $\varepsilon_Y$. It restricts to zero off Y and, in an oriented closed ambient <manifold>, represents the <Poincare dual> of Y with the normal-first induced orientation.
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