Hyper-Kähler manifolds (Q2771289)

This is a nice survey article on some aspects of the theory of hyper-Kähler manifolds. At the beginning, the author describes examples of hyper-Kähler manifolds obtained (mostly by physicists) at the end of the 70's of the last century. Then he discusses the hyper-Kähler quotient procedure for constructing such manifolds. Many moduli spaces arising in gauge theory admit hyper-Kähler structures. This is illustrated in the article by considering the moduli spaces of the Nahm equations, self-dual equations on a Riemann surface, and monopoles. The author discusses also hyper-Kähler structures occurring on coadjoint orbits of compact complex Lie groups as well as the twistor method for obtaining hyper-Kähler manifolds. Since the above mentioned techniques lead usually to non-compact manifolds, the author pays special attention to the construction of compact hyper-Kähler manifolds and presents some known results on the topology of such manifolds.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00021].