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I am playing around with the coarea formula and came across the problem of finding the Jacobian of the exponential map. Let $G$ be a compact, semisimple Lie group with associated Lie algebra $\...

$\newcommand{\id}{\operatorname{Id}} \newcommand{\R}{\mathbb{R}} \newcommand{\TM}{\operatorname{TM}} \newcommand{\Hom}{\operatorname{Hom}} \newcommand{\Cof}{\operatorname{Cof}} \newcommand{\Det}{\...