The interior and the exterior of the image of the exponential map in classical Lie groups

AbstractWe give a simple description of the interior, the exterior, and the boundary of the image of the exponential map for each of the following classes of complex Lie groups: GLfnCSLfnCOfnCSpf2nC and also for each of their real forms. There is one exception: namely for special unitary groups we are not able to describe, in general, the interior and the boundary of the exponential image. In the cases GLfnR and SLfnR the results are due to M. Nishikawa, who has also handled the case of real orthogonal groups O(p,q) when 1⩽p⩽q⩽3