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Journal of Lie Theory, 7(2), 171-199 (1997)
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On the exponentiality of real Lie groups

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D. Dokovic and K. H. Hofmann

Department of Pure Mathematics

University of Waterloo

Waterloo, Ontario N2L 3G1

Canada

dragomir@herod.uwaterloo.ca Fachbereich Mathematik

Technische Hochschule Darmstadt

Schlossgartenstr. 7

D-64289 Darmstadt

Germany

hofmann@mathematik.th-darmstadt.de

**Abstract:** The present knowledge of the structure of the exponential function of a real Lie group is surveyed. The emphasis is on the image of the exponential function: Which powers of a group element are contained in it, when is it dense, when does it fill the group? Some so far unobserved errors in the literature are pointed out, results are described, and some conjectures are formulated.
**Keywords:** Lie groups, Lie algebras, exponential map, exceptional Lie groups, Lie semigroup

**Classification (MSC91):** 22E10, 22E15, 22--02, 22E60

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