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It is know that in order to have ${\cal N}=1$ 4D compactification of M-theory or 11D SUGRA, one has to take the internal space to be a manifold of $G_2$ holonomy. Moreover, such manifolds are considered as possible target spaces of Topological M-theory.

Could anybody recommend a review of geometry and topology of 7-folds of $G_2$ holonomy? I am a physicist, so the reviews written by physicist or at least for physicists are most welcome.

This here is good;

Thanks, but the discussion there is very sketchy. Do you know of any more detailed introductions?

There are detailed discussions in the mathematical literature.But the "reviews written by physicist or at least for physicists" that you ask for are all at least this sketchy.

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