TITLE: Foliation with trivial leaf holonomy
QUESTION [6 upvotes]: In 1960, R. Hermann showed the following:
Theorem Let $M$ be a manifold with a foliation $F$ and a bundle-like metric, if all leaves are compact and the holonomy group of each leaf is trivial, then $M/F$ is a smooth manifold. 
(It is the partially result of the main theorem on Hermann, R., On the differential geometry of foliations, Ann. Math. (2) 72, 445-457 (1960). ZBL0196.54204.)
Q If we drop the condition on  bundle-like and admit the trivial holonomy group, can we get the same result? That is to say: 
Let $M$ be a manifold with a foliation $F$, if all leaves are compact and diffeomorphism to each other,   and the holonomy group of each leaf is trivial, is it true that  $M/F$ is a smooth manifold? Any reference is welcome.

REPLY [4 votes]: This follows from Theorem 2 in Thurston's 1974 paper "A generalization of the Reeb stability theorem", at least if $H^1(L,R)=0$.
https://core.ac.uk/download/pdf/82172971.pdf