This is the second of two papers about metrics of holonomy G2 on compact 7-manifolds. In
our first paper [15] we established the existence of a family of metrics of holonomy G2 on a
single, compact, simply-connected 7-manifold M, using three general results, Theorems A, B
and C. Our purpose in this paper is to explore the theory of compact riemannian 7-manifolds
with holonomy G2 in greater detail. By relying on Theorems AC we will be able to avoid the
emphasis on analysis that characterized [15], so that this sequel will have a more topological …

The list of possible holonomy groups of Riemannian manifolds given by Berger [3] includes
three intriguing special cases, the holonomy groups G2, Spin (7) and Spin (9) in dimensions
7, 8 and 16 respectively. Subsequently [1] it was shown that Spin (9) does not occur as a
nonsymmetric holonomy group, but Bryant [5] showed that both G2 and Spin (7) do occur as
non-symmetric holonomy groups. Bryant's proof is a local one, in that it proves the existence
of many metrics of holonomy G2 and Spin (7) on small balls in R7 and R8 respectively. He …