Instanton moduli on the quaternion Kähler manifold of type ${mathbf G_2}$ and singular set

We prove the completeness of an instanton moduli space on quaternion-K?hler manifold . A point in the boundary of the moduli represents an ASD bundle with a particular singular set. It is shown that the singular set is a quaternion submanifold of and the Poincaré dual of the homology class represented by is the second Chern class o f the instanton bundle. Received: 4 July 2000 / Published online: 2 December 2002 Current Address: Faculty of Mathematics, Kyushu University, Ropponmatsu, Fukuoka, 810-8560, Japan (e-mail: nagatomo@math.kyushu-u.ac.jp)