TITLE: Automorphism group of compact almost complex manifold
QUESTION [7 upvotes]: Does the automorphism group of a compact almost complex manifold carry a (canonical) Lie group structure? Part 3 of Theorem 4.1 in
*"The automorphism group of a homogeneous almost complex manifold" by J. Wolf (link at AMS site) says that in a specific group-invariant setting the automorphism group is compact if and only if the almost complex structure is not integrable. Is this a general phenomenon?

REPLY [8 votes]: See Kobayashi, Transformation Groups, Theorem 4.1 page 16, where the theorem is proved that the group of automorphisms of a smooth compact almost complex manifold is a finite dimensional Lie group acting smoothly.