New topological constructions in toric geometry and topology

Tony Bahri
Rider University, Lawrenceville NJ 08468, U.S.A.


Certain natural subspaces of a product of CW complexes, called polyhedral products, play an important role in a variety of different fields including: toric varieties, toric manifolds/orbifolds, intersections of quadrics, homotopy theory, algebraic combinatorics complements of subspace arrangements, robotics and group theory. The talk will survey certain combinatorics based constructions on polyhedral products which allow for a description of the cohomology rings of certain families of toric manifolds in a particularly compact form. The new constructions will be related to a generalization of the basic Davis- Januszkiewicz construction of toric manifolds. This report is based on joint work with Martin Bendersky, Fred Cohen and Sam Gitler.

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