ABSTRACT
This chapter focuses on quaternionic Kahler quotient. It also discusses hyperKahler and 3-Sasakian quotients. A quaternionic Kahler structure on a 4n-dimensional manifold M consists of a metric [g] and real rank-three subbundle Lie group G of End TM preserved by the Levi-Civita connection and locally generated by almost-Hermitian structures I, J, K behaving under composition like the multiplicative pure imaginary quaternions. The two-forms defined by the metric and I,J,K are now globally defined symplectic forms. If a group G acts preserving the hyperKahler structure, then in good cases we have moment maps for these symplectic structures. The chapter shows that a slight refinement of the Sjamaar-Lerman decomposition of M induces a description of the quotient as a union of manifolds. It provides a sufficient condition for a piece in the decomposition to have a Kahler covering space.
