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Lie Groups are Groups that are additionally smooth manifolds such that the multiplication and the inverse maps are smooth.

3 votes
1 answer
991 views

Lower bound for Jacobian of matrix exponential map near origin

What is a lower bound for the Jacobian of the exponential map from the skew-symmetric matrices to the orthogonal matrices near the origin?
3 votes
3 answers
471 views

Lower bound on the volume of a delta-ball in the orthogonal group O(n) of the type f(n)*delt...

Is there a lower bound on the volume of a delta-ball in the orthogonal group O(n) of the type f(n) * delta^{n(n-1)/2}? For which f(n)? How can it be proven? n(n-1)/2 is the number of degrees of freed …