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(2010 / vol.12 / no.1)
Moment-angle manifolds and complexes
Taras Panov
Pages. 43-69   



These are notes of the lectures given during the Toric Topology
Workshop at the Korea Advanced Institute of Science and Technology
in February 2010. We describe several approaches to moment-angle
manifolds and complexes, including the intersections of quadrics,
complements of subspace arrangements and level sets of moment
maps. We overview the known results on the topology of
moment-angle complexes, including the description of their
cohomology rings, as well as the homotopy and diffeomorphism types
in some particular cases. We also discuss complex-analytic
structures on moment-angle manifolds and methods for calculating
invariants of these structures.



1. Moment-angle manifolds from polytopes
2. Other constructions of the moment-angle manifold
3. Topology of monent-angle complexes
4. Complex-analytic structures on moment-anlge manifolds