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I'm reading the article of equivariant cohomology with generalized coefficients by Kumar and Vergne and I have this question from that article Let G be a compact lie group with lie algebra $\mathfrak{...

Let $f,g:\mathbb{R}^m \to \mathbb{R}^n$ be two smooth functions and let $k$ be a strictly positive integer. Write $f \sim_k g$ if at each point in the domain, the determinants of all $k \times k$ ...