Abstract
In toric topology one associates with each simplicial complex on vertices two key spaces, the Davis–Januszkiewicz space and the moment-angle complex , which are related by a homotopy fibration . A great deal of work has been done to study the properties of and , their generalizations to polyhedral products, and applications to algebra, combinatorics, and geometry. Chap. 1 surveys some of the main results in the homotopy theory of these spaces. Chap. 2 breaks new ground by initiating a study of the map . It is shown that, for a certain family of simplicial complexes , the map is a sum of higher and iterated Whitehead products. Bibliography: 49 titles.
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