Moment-angle manifolds and complexes. Lecture notes KAIST'2010

TL;DR

This lecture note overview discusses various approaches to moment-angle manifolds and complexes, their topological properties, complex structures, and methods for computing invariants, contributing to the understanding of their geometric and algebraic features.

Contribution

It provides a comprehensive overview of multiple methods and known results on the topology and complex structures of moment-angle manifolds and complexes.

Findings

Descriptions of cohomology rings of moment-angle complexes

Classification of homotopy and diffeomorphism types in specific cases

Methods for calculating invariants of complex-analytic structures

Abstract

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.