Working Seminar on Symplectic/Contact Geometry/Topology 

14/02/2012, 10:30 — 11:30 — Room P4.35, Mathematics Building
Rosa Sena Dias, CAMGSD/IST

Hyperkähler manifolds - II

Hypertoric manifolds are $4n$ dimensional hyperkähler manifolds admiting a tri-hamiltonian ${𝕋}^n$ action. We describe a construction of such manifolds as quotients of ${ℂ}^{2d}$ by subtori of ${𝕋}^d$. This construction mimics Delzant's construction of toric Kahler manifolds as quotients of ${ℂ}^d$ by subtori of ${𝕋}^d$. We will discuss relations between the two constructions and explain how to use the hyperkahler version to give a description of the hyperkähler metric in hyper action-angle coordinates.

Main reference: R. Bielawski and A. Dancer, The geometry and topology of toric hyperkähler manifolds

See also

https://www.math.tecnico.ulisboa.pt/~jmourao/ws/HK.pdf