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In Griffiths and Morgan's book "Rational Homotopy Theory and differential forms", pages 154-158, they give an example of a computation in de Rham cohomology of the minimal model of a DGA using Massey products in the complement of the (fattened up) Borromean rings in $S^3$.

A key technical ingredient in this computation is the assertion that the coboundary of the Thom class $U_N$ of the normal bundle of a submanifold $N$ with boundary $\partial N$ is the Thom class $U_{\partial N}$ of the normal bundle of that boundary: $$ \delta U_N = U_{\partial N}.$$

What I am wondering is if anyone knows of a reference for this result or even some indication of whether or not this is hard?

Note: All Thom classes are extended by zero outside their supports.

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